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Integrated Molecular Optomechanics with Hybrid Dielectric–Metallic Resonators

Cite this: ACS Photonics 2021, 8, 12, 3506–3516
Publication Date (Web):November 16, 2021
https://doi.org/10.1021/acsphotonics.1c00808

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Molecular optomechanics describes surface-enhanced Raman scattering using the formalism of cavity optomechanics as a parametric coupling of the molecule’s vibrational modes to the plasmonic resonance. Most of the predicted applications require intense electric field hotspots but spectrally narrow resonances, out of reach of standard plasmonic resonances. The Fano lineshapes resulting from the hybridization of dielectric–plasmonic resonators with a broad-band plasmon and narrow-band cavity mode allow reaching strong Raman enhancement with high-Q resonances, paving the way for sideband resolved molecular optomechanics. We extend the molecular optomechanics formalism to describe hybrid dielectric–plasmonic resonators with multiple optical resonances and with both free-space and waveguide addressing. We demonstrate how the Raman enhancement depends on the complex response functions of the hybrid system, and we retrieve the expression of Raman enhancement as a product of pump enhancement and the local density of states. The model allows prediction of the Raman emission ratio into different output ports and enables demonstrating a fully integrated high-Q Raman resonator exploiting multiple cavity modes coupled to the same waveguide.

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Introduction

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It is well understood that the electromagnetic enhancement in surface-enhanced Raman spectroscopy (SERS) (1−3) benefits both from the electromagnetic field enhancement of the pump field driving the Raman process and from the plasmonically generated local density of optical states (LDOS) enhancement for the emission at the Stokes and anti-Stokes sidebands. (4−8) It stems from a second-order perturbation description of the two-step Raman process. (6,9) The enhancement will thus depend on the exact response function of the plasmonic system at those frequencies and can be computed using the Green tensor and numerical solvers for nontrivial geometries. (6,10,11) Recently, the new formalism of molecular optomechanics was introduced, showing the analogy of SERS with cavity optomechanics. (12) It describes the Raman process as an optomechanical interaction between a localized plasmonic resonance and a molecule’s nuclear motion. The coupling of light and motion stems from a dispersive shift of the plasmonic resonance upon the molecule’s vibrational displacement. (10,12−14) The cavity optomechanics viewpoint allows a consistent description of optical forces on the molecule’s vibration inducing quantum and dynamical back-action, (14) which were previously described phenomenologically as vibrational pumping and as plasmonic asymmetry factor. (15) Furthermore, with the correct description of coherence in the optomechanical interaction, new phenomena such as collective effects have been predicted, (16) and within state of the art in plasmonic nano- and picocavities, (17) one could envision promising applications such as coherent quantum state transfer (18) and entanglement between photons and phonons (19−21) at high frequencies (1–100 THz), where no cooling is required. Very recent experimental works have already demonstrated mid-IR-to-visible transduction using this scheme. (22,23)
Cavity optomechanics often operates in the so-called “resolved sideband regime”, wherein the mechanical frequency exceeds the optical linewidth. (24) This, for instance, is deemed crucial for cooling of macroscopic motion through selectively enhancing anti-Stokes scattering (25) and to reach coherent conversion from photons to phonons and back. (19−21) The molecular optomechanics equivalence would be to have access to optical resonators with linewidths narrower than the vibrational frequency of the molecular species at hand, yet nonetheless exceptionally good confinement of the electric field for large coupling to the Raman dipole. This regime is not easily reached with plasmonics, as resonators typically have quality factors Q ∼ 20, meaning linewidths larger than or comparable to vibrational frequencies (500–1500 cm–1). Conversely, conventional higher-Q dielectric resonators typically have poor mode confinement and hence poor SERS enhancement. (26) This can in principle be compensated by increasing the quality factor of the cavities to reach SERS enhancements above 104 with, for example, whispering gallery modes (WGMs) of Q ≃ 106. (27) Nonetheless, these narrow optical resonances have linewidths below 1 GHz, 2 orders of magnitudes smaller than usual Raman linewidths, and thus only enhance a small fraction of the vibrational resonance. In the last few years, hybrid photonic–plasmonic resonators have emerged, in which hybrid resonances of dielectric microcavities coupled to plasmonic antennas are used. (28−34) Theoretical and experimental evidence points at plasmonic confinement (<λ3/105) with microcavity quality factors (Q > 103). (35,36)
In this work, we report on a semiclassical molecular optomechanics model for waveguide (WG)-addressable multiresonant hybrid photonic–plasmonic resonators coupled to molecular mechanical oscillators. This work has several important novelties. First, in evaluating the SERS enhancement, previous work on hybrid resonators has generally approximated the optical system as a single Lorentzian resonance. (37) In contrast, even the simplest hybrid resonators show Fano lineshapes in their response function, (38) responsible for the SERS enhancement factors. Thus, we expect SERS in hybrids to be controlled by a spectrally complex structure in LDOS, encompassing high-Q Fano lines and a low-Q plasmon-antenna-like contribution. Our semianalytical model correctly describes these intricate response functions over the entire frequency range, requiring only parameters from the bare resonators extracted from full-wave numerical modeling. Other approaches based on the Green tensor also allow us to derive Raman enhancements for complex photonic systems but rely on fully numerical calculations (6,11) or on a quasi-normal mode formalism. (10) Second, we extend this work from simple hybrid dielectric–photonic resonators to hybrids in which a single antenna hybridizes with multiple microcavity modes. This allows further control of SERS, through the accurate engineering of the structured photonic reservoir for Stokes, pump, and anti-Stokes frequencies independently. This scenario could be achieved with any whispering gallery mode (WGM) cavity system, with free spectral ranges that match vibrational frequencies. (39,40) Finally, a main generalization of our work over earlier works is that we include input–output channels. Indeed, in prospective molecular optomechanics experiments with hybrid dielectric photonic resonators, a waveguide can be specifically and efficiently interfaced with the cavity, to address hybrid resonances. (41) Using different input and output channels opens up new scenarios for detection schemes, like, for instance, pumping from free-space and collecting the Raman scattered power distributed over one or different output waveguide ports. This means that it is important to determine the ideal pumping and collection scheme. Our semianalytical model illustrates the potential and trade-offs for waveguide-addressable hybrid photonic–plasmonic resonators for physically relevant parameters for cavities and plasmon antennas taken from full-wave numerical modeling. (42) We derive realistic and quantitative predictions for SERS enhancements that can be compared with those obtained with the usual bare plasmon nanoparticle antennas. We finally show how the hybrid resonators will be a key platform to reach lower noise THz to visible transduction using molecular optomechanics and how the transduced signal is shared between the different output ports.

Figure 1

Figure 1. Raman scattering enhanced by a hybrid dielectric–plasmonic resonator. Top: sketch of a typical system: the spectrally narrow modes of a dielectric cavity hybridize with a plasmonic antenna resulting in high-Q small-mode-volume resonances, ideal for sideband resolved molecular optomechanics. Light can couple in and out through different ports such as the free-space or waveguides. Bottom: the hybrid system can be used to enhance both the laser pump and Raman sidebands, even in the sideband resolved regime, where the linewidth of the optical resonances are narrower than the mechanical frequency Ωm.

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Hybrid Molecular Optomechanics Formalism

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We first consider a single-mode hybrid resonator composed of a plasmonic antenna coupled to a high-Q dielectric cavity (Figure 1). The model is based on semiclassical Langevin equations (12,14) where a plasmonic antenna, described as a polarizable electrodynamic dipole scatterer, is coupled to a microcavity mode, quantified by a resonance frequency, mode volume, and intrinsic damping rate. In short, this model can be reduced to a description in terms of coupled equations of motion for two harmonic oscillators. (42) The single-cavity mode is described by the field amplitude c(ω) such that |c(ω)|2 is the normalized energy contained in the mode, with a resonance frequency ωc and a damping rate κ. The excitation of the antenna is quantified by its induced dipole moment p, which derives from its polarizable nature. We assume a polarizability with resonance frequency ωa, oscillator strength β, and a total damping rate γa(ω) = γi + γrad(ω), taking into account intrinsic ohmic losses and frequency-dependent radiation losses assumed in vacuum . (43) The dynamic antenna polarizability is then given by . Similarly to the cavity mode, the antenna field will be described by the field amplitude . We consider each of the two optical resonators to be coupled to a unique port: a waveguide for the cavity mode and free space for the antenna. A vibrating molecule is placed in the hotspot of the antenna r0, and its vibration, corresponding to the stretching or compression of a specific molecular bond, is also described as a harmonic oscillator with a mechanical coordinate xm, a resonance frequency Ωm, and a decay rate Γm. The parametric Raman process is described as an optomechanical interaction between the molecule’s vibration and the optical fields at its position. (12,14) The Langevin equations for the three harmonic oscillators (antenna, cavity, and mechanical modes) are written in the rotating frame of a laser pump of frequency ωL (see the Supporting Information)
(1)
In these equations, the cavity and antenna are linearly coupled through a hybridization strength |J|. This term describes the purely electromagnetic coupling between the two resonators: the antenna driving the cavity mode or the cavity polarizing the antenna. The magnitude of J depends on the confinement of the cavity field at the antenna position parametrized by the mode volume Vc, the oscillator strength of the antenna β, as well as the orientation of the antenna with respect to the cavity field polarization. It is written as , where Vc is the effective cavity mode volume felt by the antenna , with Ẽc(r0) = ep·Ẽc(r0) the normalized mode profile of the cavity field along the antenna polarization axis ep at the position of the antenna, and simply written as Ẽc in the following. The hybrid coupling then appears as a dipolar coupling rate between the antenna dipole and the cavity field.
The optomechanical coupling arises from a modification of the antenna and the cavity resonance frequencies due to the vibration of the molecule and is described by the optomechanical coupling strengths Ga and Gc between the molecule with either the antenna or cavity mode, and can be evaluated using first-order perturbation theory yielding (12)
(2)
where, similarly to the cavity mode, we have introduced an antenna effective mode volume , with Ẽa(r0) the normalized mode profile of the antenna, evaluated at the position of the molecule, and simply written Ẽa in the following. The overlapping optical fields of the antenna and the cavity at the position of the vibrating molecule result in a crossed optomechanical coupling whose coupling strength can be approximated as (see the Supporting Information). Two different inputs are considered for the laser pump, either a free-space input where a far-field pump directly polarizes the antenna, or, waveguide input selectively exciting the cavity modes, with input amplitude and coupling efficiencies sin,a and ηa,in for the antenna, and sin,c and ηin,c for the cavity mode. The input amplitudes are normalized such that |sin|2 is the optical power entering at a given port. Fext describes the input mechanical fields, which is here considered to be only thermal fluctuations. We thus arrive to the same coupled equations as derived by Roelli et al., (12) however extended to take into account multiple optical modes and by adding the framework of input–output theory to the equations of motion, that can model different input and output channels. We note that while the equations and phenomena considered here are classical, they could readily be extended to include quantum fluctuations by introducing noise terms with appropriate correlators.
In the present work, we are only interested in the low-cooperativity regime, which is the most experimentally relevant, (12) and we can thus neglect the back-action of the optical fields on the mechanical resonance, i.e., consider only thermal–mechanical fluctuations xm due to Fext. The optical resonator amplitudes in the third equation of eq 1 will then be neglected, which discards the laser quantum back-action as well as dynamical back-action on the mechanical mode. The noise spectral density of the molecule’s vibration is then given by the quantum Nyquist formula (44)
(3)
with the mean phonon occupation for a bath at temperature T and the zero point amplitude xzpf. These mechanical fluctuations will translate into optical Raman signal through the optomechanical coupling with the antenna and cavity modes as described by the two remaining Langevin equations for the optical fields. These can be linearized by decomposing the fields in a steady state plus a fluctuating part, a → α̅a + a, c → α̅c + c, and xm → x̅m + xm. Finally, the small frequency shift due to the steady-state mechanical displacement x̅m ∼ 0 is absorbed in the definition of ωa and ωc. The steady-state solutions were found by setting a = c = 0, and we get
(4)
They correspond to the solution of a Rayleigh scattering process. The susceptibilities of the bare cavity mode χc and antenna mode χa are
(5)
The antenna and cavity response are modified by the hybrid coupling J, which yields new hybridized susceptibilities χc′ and χa′ for the two optical modes
(6)
They can be seen as the bare constituents susceptibilities, dressed by an infinite series of antenna–cavity scattering events. The antenna having a very broad response compared to the cavity, the hybridized susceptibility χa′, will display a Fano resonance at the frequency of the cavity. (45)
The fluctuating part of the field (Ω ≠ 0), responsible for the Raman scattering, is expressed in the frequency domain, and we keep only terms that are first order in the fluctuations (i.e., xma, xmc → 0)
(7)
Note that the fluctuations are evaluated at the frequency ωL + Ω. To evaluate the Stokes or anti-Stokes sidebands, we will later set Ω = ∓Ωm. The right-hand side of the equations shows that the source terms for the optical fluctuations arise from a sum of direct and crossed optomechanical coupling with the mechanical vibration. The first is given with a rate Ga or Gc, and the second through crossed optomechanical coupling Gcross; they are directly proportional to the steady-state solutions obtained previously. Both of these processes are described by an effective optomechanical coupling Ga,ceff = Ga,cα̅a,c + Gcrossα̅c,a taking both the coupling rate and the steady-state solutions into account. We finally obtain the solutions for the fluctuations
(8)
with all of the susceptibilities evaluated at the emission frequency ωL + Ω. The antenna and cavity fluctuations a and c appear as a transduction of mechanical fluctuations xm with a modified response due to the hybrid coupling characterized by J. The case with only a bare antenna corresponding to the usual SERS experiments is retrieved by setting J = Gcross = 0, yielding
(9)
Following the optomechanical formalism put forward in ref (12), with no back-action on the mechanical mode, we have arrived at a set of coupled classical equations where the optical fluctuations of the modes (inelastic process ω ≠ ωL) are driven by mechanical vibrations of the molecule.
Raman spectra scattered by the antenna to the far-field Sant and the cavity to the waveguide Scav can be immediately expressed as
(10)
where ωD is the frequency of detection.
To obtain Raman enhancements factors, the spectra are normalized by the emission of the molecule in the homogeneous medium, in the absence of a resonator, given for the same excitation and collection conditions. This reference situation is modeled as the scattering of the Raman dipole of the molecule, (6) in which
(11)
where Einc is the incident field at the position of the molecule (see the Supporting Information). Using Larmor’s formula, (46) one obtains the reference Raman scattered spectrum for the molecule in a homogeneous medium of index n = 1
(12)
where we have replaced |xm|2 → Sxx.
By replacing a and c by their expression of eq 8 and using eq 2, one can write the Raman spectrum of the antenna and the cavity as the product of three terms
(13)
i.e., the reference spectrum Sref enhanced both by a pump enhancement term and a collected LDOS (LDOSC) in either output port. The pump enhancement is given by
(14)
and corresponds to the field enhancement due to the optical hotspots compared to the incident field. The total field at the molecule’s position (neglecting the incident field direct contribution) shows a coherent mixing of cavity and antenna contributions. The Raman emission is also enhanced by the collected LDOS, which, depending on the assumed collection channel, i.e., through the free-space or the waveguide port, reads
(15)
The total LDOS obtained by summing these two expressions can be cast as
(16)
given by the sum of the LDOS of the hybridized antenna and cavity modes, along with a term arising from coherent interaction between the two resonators. The equality between the two equations is obtained only if ηout = 1, otherwise the intrinsic losses need to be added.
Both LDOSC expressions of eq 15 show a coherent coupling between antenna and cavity characterized by the effective susceptibilities
(17)
that describe the hybrid response of each resonator in the presence of two coherently summed driving terms. They contain all of the spectral information governing the Raman spectra. Indeed, it can be shown that the pump enhancement of eq 14 can also be written as a function of the effective susceptibilities when pumping only through one port (free space or waveguide). The final Raman spectrum will then be a product of the effective susceptibility squared magnitudes evaluated at the pump and Raman-shifted frequencies
(18)
Using the molecular optomechanics formalism, we retrieve the second-order perturbation theory result relating the surface-enhanced Raman enhancement to the product of enhancement factor at the pump and emission frequencies. (4−6) A fine tuning of the antenna–cavity detuning is then essential to maximize the Raman enhancement of the hybrid. We have verified that the predictions of the model precisely match full-wave numerical simulation results, as shown in the Supporting Information.

Results

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Hybrid SERS Spectra

In Figure 2a, we plot the free-space Raman spectrum of an assumed Raman active species at a bare antenna Santbare(ωL, ωD), normalized by the Stokes peak amplitude of the same analyte in a vacuum environment as reference SrefStokes = Sref(ωD = ωL – Ωm). The antenna parameters are ωa/(2π) = 460 THz, γi/(2π) = 20 THz, β = 0.12 C2 kg–1 and an effective mode volume corresponding to the values of a dipole placed at 10 nm away from a 50 nm radius gold sphere. Free-space input and collection are assumed to occur via a NA = 1 objective in vacuum, i.e., collection of the radiation in the upper half-space. This results in ηout = 1/2 and excitation ηin = 1/10 due to finite scattering cross section (see the Supporting Information). The molecular vibration frequency in this example is chosen as Ωm/(2π) = 30 THz, corresponding to typical Raman shifts of 1000 cm–1, (6) with quality factor Qm = 200.

Figure 2

Figure 2. Raman spectrum enhanced by an antenna (a) as a function of the laser frequency, normalized by the Stokes emission peak of the molecules in air SrefStokes(ωL). The cross-cuts at the dashed blue and green lines correspond to (b) and (c). (b) Raman spectrum at the maximum enhancement and (c) antenna enhancement at the Stokes sideband as a function of the laser frequency. (d) Raman spectrum of the bare antenna Santbare, normalized by the Raman emission of the molecules in air Sref showing the antenna SERS enhancement as a function of the laser and detected frequencies. It is equal to the product of a pump enhancement term (e) and of a collected LDOS enhancement term (f). The case of a hybrid antenna–cavity resonator is given in (g)–(l), exhibiting narrow Fano resonances both in the Raman spectrum and in the pump and LDOS enhancements. See text for parameters.

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The antenna-enhanced Raman spectrum shows two sidebands appearing as diagonals at ωD = ωL ∓ Ωm, i.e., the anti-Stokes and Stokes sidebands observed at the laser frequency shifted by the mechanical vibration resonance frequency. A vertical cut at the maximum intensity (blue dashed line) is shown in Figure 2b, representing a Raman spectrum at laser frequency fixed to the value at which the Stokes signal is most enhanced. The detected Stokes signal when scanning the laser frequency (green diagonal dashed line, detection frequency shifting in concert with the laser frequency) is shown in Figure 2c. As in usual SERS experiments, (6) the maximum enhancement is achieved when the pump frequency is set at , resulting in the best trade-off between pump enhancement taking place at ωL = ωa, and emission enhancement occurring at ωD = ωa. With the antenna and molecule position considered here, we obtain Raman enhancements on the order of 104, limited only by the effective mode volume of the antenna. We point out that this moderate Raman enhancement is only a consequence of the modest antenna parameters chosen in this work and that Raman enhancements up to 1010 are expected with state-of-the-art plasmonic antennas exhibiting nanometer-scale gap modes. (35,47) Indeed, for plasmonic antennas, and for the hybrids, the Raman enhancement will scale inversely as the mode volume of the antenna as it is shown in the Supporting Information. The effect of the photonic system is better visualized in Figure 2d, where we plot again the antenna-enhanced Raman spectrum Santbare, but now normalized to the reference Raman spectrum Sref(ωD, ωL), to remove the dependence on the chosen mechanical vibration. We thus obtain the antenna enhancement compared to the homogeneous medium case for any pump and detection frequency. As it was derived for the hybrid case, the bare antenna Raman enhancement can be cast as a product of the pump enhancement |Etot/Einc|2 and the collected LDOS, shown respectively in Figure 2e,f. Pump and LDOS enhancements for the bare antenna are obtained from eqs 14 and 15 by setting J = Gcross = 0. The pump enhancement depends on the laser frequency and the LDOSC on the detected frequency. High enhancements of the Raman process are obtained by enhancing both the pump at ωL and the LDOS at ωL + Ωm, and are thus usually achieved with broad antenna resonances such that γa > Ωm, placing them by default on the sideband nonresolved system.
By a careful choice of parameters, the hybrid resonator allows to go beyond the limitation of sideband nonresolved optomechanics, yet obtain large SERS enhancement factors. The same figures of Raman scattering spectra in the case of a hybrid antenna-dielectric resonator are shown in Figure 2g–l, with a cavity red-detuned from the antenna by the mechanical vibration frequency ωc/(2π) = (ωa – Ωm)/(2π) = 430 THz corresponding to the Stokes sideband of the antenna, and a mode volume Vc = 10λ3 and quality factor Qc = 103. The main new feature is the appearance of a Fano resonance close to the cavity frequency, due to the interference of the coupled broad antenna resonance and the fine cavity resonance. This Fano feature is inherited both by the Raman spectrum, Figure 2h, and in the Stokes enhancement, Figure 2i, which show the capability of the hybrid system to obtain high enhancement with a high-Q resonance. Interestingly, the maximum Stokes enhancement is obtained for a laser tuned at ωL = ωa, the hybrid resonator allowing to enhance the pump with the antenna resonance, and the emission with the cavity resonance. Better insight follows from the Raman enhancement of the hybrid compared to homogeneous medium and shown in Figure 2j, which again is the product of a pump enhancement (Figure 2k) at the laser frequency and a collected LDOS enhancement (Figure 2l) at the detected frequency. Both quantities display a broad antenna-like resonance and a narrow Fano resonance arising from mixing with the cavity-like mode.

Choice of Optimum Read Out Scheme

In the rest of the article, we will focus on the Stokes (or anti-Stokes) enhancement curves, as the ones shown in Figure 2c,i, i.e., the detected frequency will be fixed at ωD = ωL ∓ Ωm as the laser frequency is scanned. In the case of the hybrid, the two different input and two different output ports result in four different Raman spectroscopy scenarios depending on whether the pump and collection are performed through the waveguide or in free space. The Stokes enhancement factors for the four different cases are presented in Figure 3, with the bare antenna response plotted in the dashed curve in panel a. The parameters are the same as in Figure 2, with again a cavity red-detuned from the antenna by the molecule’s vibration frequency, ωc = ωa – Ωm. The following observations can be made. First, the simultaneous excitation and read-out through the waveguide acts as a strong spectral filter at the cavity resonance. Since pump and Raman signal are at shifted frequencies, this filtering action intrinsically results in low overall SERS enhancements, 3 orders of magnitude below that offered by just an antenna in free space. Conversely, excitation and collection from free space result in a large SERS enhancement, roughly on the same scale as the SERS enhancement that the bare antenna provides, but still with improved numbers due to the simultaneous matching of pump and emission frequencies with one of the two resonators. However, the cavity mode elicits strong Fano features both when the pump and when the Stokes frequency go through cavity resonance. Finally, we consider the “mixed port” cases where either the pump goes via the waveguide and collection is via free space, or vice versa. Remarkably, the strongest pump field enhancement is reached when pumping through the waveguide and at cavity resonance ωL ≈ ωc. For the chosen strongly blue-detuned cavity, the enhancement at the Stokes-shifted frequency for scattering in free space is modest due to the large detuning from antenna resonance, but nonetheless, the joint effect is a strong SERS peak. Conversely, detection through the waveguide requires tuning ωL = ωc + Ωm. The pump field is resonantly enhanced by the antenna, while the Raman signal collection into the waveguide is enhanced over a narrow band around ωD = ωc. The overall enhancement is similar to that in the reversed port choice to within a factor 2. This result can appear surprising since only one of the two configurations is doubly resonant and one would expect better enhancement factors in this case. However, the loss of enhancement due to a detuned antenna is compensated by the better output coupling efficiency for the antenna compared to the input coupling, ηin = (1/5)ηout (see the Supporting Information). The waveguide allows better incoupling efficiencies than the antenna, but the collection efficiency can be, potentially, as good for the two.

Figure 3

Figure 3. Stokes enhancement for the four different combinations of input–output as depicted on the sketches. Each Stokes enhancement (iii) is obtained as the product of the pump enhancement at ωL (i) and the collected LDOS at ωD = ωL – Ωm (ii) for the given input and output, respectively. The bare antenna response is plotted in the dashed curve in panel (a). The parameters are the same as in Figure 2.

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To summarize, the hybrid system allows reaching Stokes enhancements of the same order of magnitude as the bare antenna case, but with much larger quality factors. Of particular interest for sideband resolved read out of vibrations is the case with collection through the waveguide where the Raman scattering is filtered by the narrow cavity resonance with enhancement factors similar to the case of free-space input and output. This allows us to explore the sideband resolved regime with high Raman enhancement.

Detuning Dependence

While coarsely speaking, the antenna and cavity frequencies need to be detuned by the mechanical vibration frequency ωa – ωc = ±Ωm to obtain the best enhancement factors, the fact that the enhancement is due to the product of Fano lineshapes imposes a finer analysis of the optimal detunings that are needed, and it is presented in the following. We focus here on the case where the cavity is red-detuned with respect to the antenna, and thus enhancing the Stokes sideband. Anti-stokes enhancement, requiring an inversed antenna–cavity detuning will be analyzed next.
Figure 4 presents the Stokes enhancement factor for the two different collection ports, when pumping through free space. The cavity–antenna detuning Δca = ωc – ωa is changed by scanning the cavity frequency around ωa – Ωm, corresponding to the case considered in Figure 2. The cavity frequency is scanned by steps of 16κ, with, for each frequency, the Stokes enhancement shown as the product of the pump enhancement and LDOSC. Panels b and d show the maxima of the Stokes enhancement as a function of detuning, with each cross corresponding to the maximum Stokes enhancement of the same color in panels a and c, respectively. For both collection through free space or in the waveguide, the maximum achievable Stokes enhancement is obtained close to the intuitive detuning ωc = ωa – Ωm, but with some shift due to the Fano lineshapes. In the case of the waveguide output, an important contributor to the shift comes from an intrinsic asymmetry in antennas, namely, the fact that radiative losses into free space decrease at low frequencies, which facilitates a higher overall coupling into the waveguide. Concerning the tuning sensitivity, since one of the two resonances in play is still the broad antenna resonance, the needed precision in the antenna–cavity detuning remains on the order of the antenna linewidth.

Figure 4

Figure 4. Influence of the cavity–antenna detuning Δca on the Stokes enhancement for free-space input/output (a) and free-space input and waveguide output (c). The antenna frequency is fixed at ωa/(2π) = 460 THz, and the cavity frequency is scanned around ωa – Ωm in steps of 16κ. The maximum Stokes enhancement for each detuning is shown in (b) and (d) for the two collection cases, with the colored crosses corresponding to the respective colored plots in (a) and (c).

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Choice of Cavity Parameters

An important question is how to choose the most appropriate cavity quality factor to reach the highest Raman enhancements. Aside from matching to the vibrational Q, the cavity Q will modify the in- and outcoupling ratio into the waveguide compared to free space. This is analyzed in Figure 5, where we plot the maximum pump enhancement and collected LDOS of eqs 14 and 15 as a function of the cavity quality factor Qc. The antenna and cavity frequencies are ωa/(2π) = 460 THz, and ωc = ωa – ωm, corresponding to the double resonant case for simultaneous pump and collection enhancement. Panels a and c first show the case of a fixed-mode volume Vc = 10λ3 (as used throughout this work). It can be seen that for free-space input and output, the enhancement factors are increased for higher Qc values since the Fano resonances sharpen to higher maximum values. Instead, for the case of waveguide input and output, there is an optimum at Qc ≃ 1000 both for the pump enhancement and LDOSC. This is due to a trade-off with the cavity coupling efficiency that deterioriates for high Qc while for too small Qc, the LDOS enhancement will be small. The exact value of the best Qc depends on the cavity mode volume Vc, which determines the hybrid coupling efficiency through |J|2 ∝ 1/Vc. For reference, we also show the case of constant Purcell factor Qc/Vc cavity in Figure 5b,d. It is seen that the LDOS and pump enhancement are mostly constant for the whole range of Purcell factors, showing that the LDOS of the hybrid resonances only depend on the ratio Qc/Vc. (42) This ratio is also proportional to |J|2/κ, which appears in the denominator of eq 6 with χc(ωc) ∝ Qc. This term dictates the hybrid interaction rate, and for constant Qc/Vc, the interaction rate remains unchanged.

Figure 5

Figure 5. Maximum achievable pump enhancement (a, b) and LDOSC (c, d) as a function of the cavity quality factor Qc for both input and output configurations; (a) and (c) are given for a fixed-mode volume Vc = 10λ3, whereas (b) and (d) are given for a constant-cavity Purcell factor Qc/Vc. The antenna frequency is ωa/(2π) = 460 THz, and the cavity frequency is fixed at ωc = ωa – Ωm. The horizontal dotted line corresponds to the free-space case with only the bare antenna.

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Anti-Stokes Detection

Enhancement of the anti-Stokes sideband can also be achieved with the hybrid resonator. To achieve the best collection in the waveguide, the cavity now needs to be blue-detuned with respect to the antenna mode. As shown in Figure 6, the enhancement is in this case slightly smaller than for the Stokes enhancement case. This is due to the increased radiative losses γrad of the antenna at the (blue-shifted) collection frequency and a stronger emission from the reference dipole scaling as ωD4 as seen in eq 12. This has an impact for both collection paths, which still results in a comparable enhancement factor for the waveguide collection case compared to the free-space collection.

Figure 6

Figure 6. Anti-Stokes enhancement for different cavity–antenna detunings. The antenna is now red-detuned (ωa = 400 THz) to enhance the pump, and the cavity frequency is scanned around the anti-Stokes sideband (ωa + Ωm) in steps of 16κ. The input is in free space, and the collection is either in free space (a) or in the waveguide (b).

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Multimode Cavities

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We have shown that the hybrid with a single dielectric mode is able to provide integrated collection of the Raman signal with good enhancement factors for both Stokes and anti-Stokes. Nevertheless, a fully integrated operation is prevented by the sideband resolution of the cavity that prevents from enhancing both the pump and the collection simultaneously through the waveguide. This issue can be resolved by working with multiple high-Q cavity modes, which allow both pump and collection enhancement. For instance, whispering gallery mode cavities provide multiple cavity modes addressable through the same waveguide. In this way, one could envision using two different cavity resonances to simultaneously enhance the pump and collection, by tuning the mode spacing to match the mechanical resonance frequency. The resulting Stokes enhancement factors are shown in Figure 7 for a hybrid with two cavity modes coupled to the same waveguide and an antenna coupled to free space. It can be shown that for multiple-resonant systems, the Raman enhancement can still be written as a product of the pump field enhancement by the hybrid and the collection LDOS in a given port, similarly to eq 13. We compare the cases of only free space addressing (a) with the fully integrated case (b). The first cavity mode is red-detuned, to enhance the collection, and is labeled C. The second cavity will serve to enhance the pump and is labeled P. Both cavity modes are then red-detuned compared to the antenna so as to work in the optimal regime where the radiative losses of the antenna are reduced. We have then from blue to red: ωa/(2π) = 460 THz, ωP/(2π) = 415 THz, and the frequency of the cavity mode use for collection scanned around the Stokes sideband of the former ωC ≃ ωP – Ωm in steps of 1.1κ. We can see that the use of two cavity modes allows simultaneously a pump enhancement and an LDOS enhancement as shown in Figure 7b. This allows fully integrated Stokes enhancement factors that reach values equivalent to the Stokes enhancements of the bare antenna free-space configuration (in the order of 104 as seen in Figure 3a). This is furthermore obtained with high-Q resonances deep in the sideband resolved regime. Although the final enhancement─product of two hybridized cavity susceptibilities─necessitates fine frequency tuning on the order of κ, it allows for fully integrated Raman scattering with unspoiled enhancements.

Figure 7

Figure 7. Stokes enhancement with a two-mode cavity and an antenna hybrid. The antenna is blue-detuned ωa/(2π) = 460 THz with respect to both cavity modes. The first cavity mode serves as pump enhancement at ωP/(2π) = 415 THz, and the Stokes sideband emission is enhanced by the second cavity mode, which is scanned around ωP – Ωm. We compare the cases with free-space-only (a) or waveguide-only (b) input and output. The Stokes enhancement is again the product of a pump enhancement factor and the collected LDOS. The inset in (b) shows a close-up of the best Raman enhancements close to ωL = ωP.

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Outlook

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The analogies with cavity optomechanics have resulted in exciting predictions of new phenomena in the field of SERS. Most of these new applications, such as dynamical back-action (12) and low-noise THz to optical transduction, (18) benefit from both a good optomechanical coupling, and sideband resolution, i.e., an optical linewidth smaller than the Raman shift. This implies having a resonator that has both small mode volumes and high-Q resonance. Hybrid dielectric and plasmonic resonances can achieve simultaneously these two requirements, exploiting both the small volume of a plasmonic antenna and the spectral confinement of dielectric cavities, with tunable parameters as a function of the detuning between the two resonators. (42)
We have developed a new formalism based on molecular optomechanics that allows us to calculate absolute Raman enhancement factor of a multimode hybrid system from simple parameters of the bare constituents. This represents in practice a substantial saving in computation time. Indeed, on the basis of a library of properties of N cavities, and M antennas, which will require N + M simulations, we can predict the performance for all N × M combinations, and at any relative placement without further simulation. We intend this to be contrasted to full-wave-only approaches that will require each geometry to be simulated (N × M calculations, times the number of relative positions). The expressions obtained in this model explicitly show the interplay of pump and LDOS enhancement factors. We have then demonstrated that using experimentally available (36) hybrid systems, one can reach Raman enhancement factors equivalent to the bare plasmonic case, but in the sideband resolved regime, with optical linewidths orders of magnitudes smaller than the mechanical frequency. Additionally, our formalism correctly describes the coupling to different input and output ports, and we show that although optimal excitation and collection is reached through the antenna port, Raman enhancement for collection in the waveguide remains on the same order of magnitude. We have discussed the best choice of cavity parameters to optimize the Raman enhancement from the hybridized resonance. We showed that, for a given cavity mode volume, there is an optimal quality factor Qc resulting from the trade-off of good incoupling and outcoupling rates and the strength of the cavity response function. More precisely, for realistic mode volumes of Vc = 10λ3, (35) best integrated results are obtained for Qc ∼ 1000, easily accessible for any dielectric cavity. (36,48) Our model is readily applicable to experimental implementation using hybrid systems with dipolar plasmonic resonances. Best performances are predicted for antennas positioned near the cavity antinodes, increasing the hybrid coupling J, and for molecules as close as possible to the antenna hotspots, using, for example, self-assembled monolayers. (49) Finally, an efficient and fully integrated platform is proposed using simultaneously two different cavity modes, hybridized with a plasmonic antenna and coupled to same waveguide, each enhancing the pump and the collection respectively. Although we have here focused on the peak enhancement factors, the opportunities for Fano lineshapes are particularly exciting in quantum optomechanical applications employing reservoir engineering. (50) Recently, Roelli et al. (18) proposed molecular optomechanics for transduction of IR and THz radiation to visible light, with two very recent works showing experimental evidence for this. (22,23) By making use of Fano dips, it becomes possible to inhibit noise processes such as laser back-action-induced noise, i.e., vibrational pumping, greatly enhancing the signal-to-noise ratio for mechanical to visible transduction, as sketched in Figure 8a. This would allow us to push recent efforts in IR/THz to visible transduction (22,23) toward the quantum regime. With careful frequency tailoring, fully integrated quantum transduction could be obtained using multiple cavity modes, one inhibiting the Stokes and two enhancing the pump and the up-converted anti-Stokes photon. This will be the topic of future studies. In Figure 8b,c, we show an example of anti-Stokes enhancement, when pumping the system through the waveguide. The fraction of anti-Stokes photons emitted into the WG (fully integrated case) reaches values above 80%, with high Raman enhancement values above 103. Emission fractions into the WG above 95% can be easily obtained by increasing the Qc/Vc ratio of the cavity by a factor 4 compared to our parameters, e.g., using a cavity with Qc = 4000. In addition, we note that the similarities of our three-mode optomechanical model in this work with the model of photonic-molecule optomechanics (51,52) can lead to immediate applications, already demonstrated in more traditional optomechanical systems, such as phonon lasers (53−56) and unconventional single-photon devices. (57−60) Our semianalytical classical model is formulated such that it is easily translated into quantum mechanical equations of motion, solvable with, e.g., the Python toolbox QuTip.

Figure 8

Figure 8. (a) Low-noise, integrated, IR-to-visible transduction using reservoir engineering. Using multiple cavity modes, one can selectively enhance the up-converted anti-Stokes while suppressing unwanted back-action noise. (b) Anti-Stokes enhancement with a two-mode cavity and an antenna hybrid. Parameters are the same as in Figure 7, with the laser now pumping the redder cavity. The red solid line corresponds to collection through the waveguide (fully integrated system), while the dashed blue line is for a collection through free space. (c) Integrated behavior: fraction of collected light into the waveguide (WG), reaching values up to 80% due to the Fano dip in the response function of the hybridized antenna.

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Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.1c00808.

  • Derivation of the Langevin equations, input–output parameters, influence of the antenna field confinement on SERS enhancement, and benchmark against full-wave simulations (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Ilan Shlesinger - Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands;  Orcidhttps://orcid.org/0000-0002-9328-1926
    • Kévin G. Cognée - Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands;  LP2N, Institut d’Optique Graduate School, CNRS, Univ. Bordeaux, 33400 Talence, France
    • Ewold Verhagen - Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands;  Orcidhttps://orcid.org/0000-0002-0276-8430
  • Author Contributions

    I.S. and K.G.C. contributed equally to this work.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work is part of the research program of the Netherlands Organisation for Scientific Research (NWO). The authors acknowledge support from the European Unions Horizon 2020 research and innovation program under Grant Agreements No. 829067 (FET Open THOR) and No. 732894 (FET Proactive HOT), and the European Research Council (ERC starting Grant No. 759644-TOPP). They also thank Javier del Pino and Philippe Lalanne for fruitful discussions and for their support.

References

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    Vibrational pumping in surface enhanced Raman scattering (SERS)
    Maher, R. C.; Galloway, C. M.; Le Ru, E. C.; Cohen, L. F.; Etchegoin, P. G.
    Chemical Society Reviews (2008), 37 (5), 965-979CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. In this tutorial review, the underlying principles of vibrational pumping in surface enhanced Raman scattering (SERS) are summarized and explained within the framework of their historical development. Some state-of-the-art results in the field are also presented, with the aim of giving an overview on what was established at this stage, as well as hinting at areas where future developments might take place.
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  16. 16
    Zhang, Y.; Aizpurua, J.; Esteban, R. Optomechanical Collective Effects in Surface-Enhanced Raman Scattering from Many Molecules. ACS Photonics 2020, 7, 1676– 1688,  DOI: 10.1021/acsphotonics.0c00032
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    16
    Optomechanical Collective Effects in Surface-Enhanced Raman Scattering from Many Molecules
    Zhang, Yuan; Aizpurua, Javier; Esteban, Ruben
    ACS Photonics (2020), 7 (7), 1676-1688CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    The interaction between mols. is commonly ignored in surface-enhanced Raman scattering (SERS). Under this assumption, the total SERS signal is described as the sum of the individual contributions of each mol. treated independently. We adopt here an optomech. description of SERS within a cavity quantum electrodynamics framework to study how collective effects emerge from the quantum correlations of distinct mols. We derive anal. expressions for identical mols. and implement numerical simulations to analyze two types of collective phenomena: (i) a decrease of the laser intensity threshold to observe strong nonlinearities as the no. of mols. increases, within very intense illumination, and (ii) identification of superradiance in the SERS signal, namely a quadratic scaling with the no. of mols. The laser intensity required to observe the latter in the anti-Stokes scattering is relatively moderate, which makes it particularly accessible to expts. We treat the system on the basis of the individual mols. and demonstrate that for ideal systems with identical mols. this approach is equiv. to a description based on collective modes. The basis of individual mols. also allows for describing in a straightforward manner more general systems where the mols. might have different vibrational properties or suffer from pure-dephasing processes. Our results show that the collective phenomena can survive in the presence of the homogeneous and inhomogeneous broadening that might influence exptl. results.
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  17. 17
    Benz, F.; Schmidt, M. K.; Dreismann, A.; Chikkaraddy, R.; Zhang, Y.; Demetriadou, A.; Carnegie, C.; Ohadi, H.; De Nijs, B.; Esteban, R.; Aizpurua, J.; Baumberg, J. J. Single-molecule optomechanics in ”picocavities”. Science 2016, 354, 726– 729,  DOI: 10.1126/science.aah5243
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    17
    Single-molecule optomechanics in "picocavities"
    Benz, Felix; Schmidt, Mikolaj K.; Dreismann, Alexander; Chikkaraddy, Rohit; Zhang, Yao; Demetriadou, Angela; Carnegie, Cloudy; Ohadi, Hamid; de Nijs, Bart; Esteban, Ruben; Aizpurua, Javier; Baumberg, Jeremy J.
    Science (Washington, DC, United States) (2016), 354 (6313), 726-729CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Trapping light with noble metal nanostructures overcomes the diffraction limit and can confine light to vols. typically ∼30 cubic nanometers. Individual at. features inside the gap of a plasmonic nanoassembly can localize light to vols. well <1 cubic nanometer (picocavities), enabling optical expts. on the at. scale. These at. features are dynamically formed and disassembled by laser irradn. Although unstable at room temp., picocavities can be stabilized at cryogenic temps., allowing single at. cavities to be probed for many minutes. Unlike traditional optomech. resonators, such extreme optical confinement yields a factor of 106 enhancement of optomech. coupling between the picocavity field and vibrations of individual mol. bonds. This work sets the basis for developing nanoscale nonlinear quantum optics on the single-mol. level.
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  18. 18
    Roelli, P.; Martin-Cano, D.; Kippenberg, T. J.; Galland, C. Molecular Platform for Frequency Upconversion at the Single-Photon Level. Phys. Rev. X 2020, 10, 031057  DOI: 10.1103/PhysRevX.10.031057
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    18
    Molecular Platform for Frequency Upconversion at the Single-Photon Level
    Roelli, Philippe; Martin-Cano, Diego; Kippenberg, Tobias J.; Galland, Christophe
    Physical Review X (2020), 10 (3), 031057CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    Direct detection of single photons at wavelengths beyond 2μm under ambient conditions remains an outstanding technol. challenge. One promising approach is frequency upconversion into the visible (VIS) or near-IR (NIR) domain, where single-photon detectors are readily available. Here, we propose a nanoscale soln. based on a mol. optomech. platform to up-convert photons from the far- and mid-IR (covering part of the terahertz gap) into the VIS-NIR domain. We perform a detailed anal. of its outgoing noise spectral d. and conversion efficiency with a full quantum model. Our platform consists in doubly resonant nanoantennas focusing both the incoming long-wavelength radiation and the short-wavelength pump laser field into the same active region. There, IR active vibrational modes are resonantly excited and couple through their Raman polarizability to the pump field. This optomech. interaction is enhanced by the antenna and leads to the coherent transfer of the incoming low-frequency signal onto the anti-Stokes sideband of the pump laser. Our calcns. demonstrate that our scheme is realizable with current technol. and that optimized platforms can reach single-photon sensitivity in a spectral region where this capability remains unavailable to date.
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    Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W. Entangling Mechanical Motion with Microwave Fields. Science 2013, 342, 710– 713,  DOI: 10.1126/science.1244563
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    19
    Entangling mechanical motion with microwave fields
    Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W.
    Science (Washington, DC, United States) (2013), 342 (6159), 710-713CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    When two phys. systems share the quantum property of entanglement, measurements of one system appear to det. the state of the other. This peculiar property is used in optical, at., and elec. systems in an effort to exceed classical bounds when processing information. The authors extended the domain of this quantum resource by entangling the motion of a macroscopic mech. oscillator with a propagating elec. signal and by storing one half of the entangled state in the mech. oscillator. This result demonstrates an essential requirement for using compact and low-loss micromech. oscillators in a quantum processor, can be extended to sense forces beyond the std. quantum limit, and may enable tests of quantum theory.
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    Palomaki, T. A.; Harlow, J. W.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W. Coherent state transfer between itinerant microwave fields and a mechanical oscillator. Nature 2013, 495, 210– 214,  DOI: 10.1038/nature11915
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    Coherent state transfer between itinerant microwave fields and a mechanical oscillator
    Palomaki, T. A.; Harlow, J. W.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W.
    Nature (London, United Kingdom) (2013), 495 (7440), 210-214CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Macroscopic mech. oscillators have been coaxed into a regime of quantum behavior by direct refrigeration or a combination of refrigeration and laser-like cooling. This result supports the idea that mech. oscillators may perform useful functions in the processing of quantum information with superconducting circuits, either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems. As yet, the transfer of an itinerant state or a propagating mode of a microwave field to and from a storage medium has not been demonstrated, owing to the inability to turn on and off the interaction between the microwave field and the medium sufficiently quickly. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mech. oscillator with amplitudes at the single-quantum level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mech. oscillator. In this quantum regime, the mech. oscillator can both store quantum information and enable its transfer between otherwise incompatible systems.
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  21. 21
    Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W. Faithful conversion of propagating quantum information to mechanical motion. Nat. Phys. 2017, 13, 1163– 1167,  DOI: 10.1038/nphys4251
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    Faithful conversion of propagating quantum information to mechanical motion
    Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W.
    Nature Physics (2017), 13 (12), 1163-1167CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
    The motion of micrometre-sized mech. resonators can now be controlled and measured at the fundamental limits imposed by quantum mechanics. These resonators have been prepd. in their motional ground state or in squeezed states, measured with quantum-limited precision, and even entangled with microwave fields. Such advances make it possible to process quantum information using the motion of a macroscopic object. In particular, recent expts. have combined mech. resonators with superconducting quantum circuits to frequency-convert, store and amplify propagating microwave fields. But these systems have not been used to manipulate states that encode quantum bits (qubits), which are required for quantum communication and modular quantum computation. Here we demonstrate the conversion of propagating qubits encoded as superpositions of zero and one photons to the motion of a micromech. resonator with a fidelity in excess of the classical bound. This ability is necessary for mech. resonators to convert quantum information between the microwave and optical domains or to act as storage elements in a modular quantum information processor. Addnl., these results are an important step towards testing speculative notions that quantum theory may not be valid for sufficiently massive systems.
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    Chen, W.; Roelli, P.; Hu, H.; Verlekar, S.; Amirtharaj, S. P.; Barreda, A. I.; Kippenberg, T. J.; Kovylina, M.; Verhagen, E.; Martínez, A.; Galland, C. Continuous-Wave Frequency Upconversion with a Molecular Optomechanical Nanocavity. 2021, arXiv:2107.03033. arXiv.org e-Print archive. https://arxiv.org/abs/2107.03033.
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    Xomalis, A.; Zheng, X.; Chikkaraddy, R.; Koczor-Benda, Z.; Miele, E.; Rosta, E.; Vandenbosch, G. A. E.; Martínez, A.; Baumberg, J. J. Detecting Mid-Infrared Light by Molecular Frequency Upconversion with Dual-Wavelength Hybrid Nanoantennas. 2021, arXiv:2107.02507. arXiv.org e-Print archive. https://arxiv.org/abs/2107.02507.
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    Aspelmeyer, M.; Kippenberg, T. J.; Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 2014, 86, 1391– 1452,  DOI: 10.1103/RevModPhys.86.1391
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    Cohadon, P. F.; Heidmann, A.; Pinard, M. Cooling of a Mirror by Radiation Pressure. Phys. Rev. Lett. 1999, 83, 3174– 3177,  DOI: 10.1103/PhysRevLett.83.3174
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    Cooling of a Mirror by Radiation Pressure
    Cohadon, P. F.; Heidmann, A.; Pinard, M.
    Physical Review Letters (1999), 83 (16), 3174-3177CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We describe an expt. in which a mirror is cooled by the radiation pressure of light. A high-finesse optical cavity with a mirror coated on a mech. resonator is used as an optomech. sensor of the Brownian motion of the mirror. A feedback mechanism controls this motion via the radiation pressure of a laser beam reflected on the mirror. We have obsd. either a cooling or a heating of the mirror, depending on the gain of the feedback loop.
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    Giannini, V.; Fernández-Domínguez, A. I.; Heck, S. C.; Maier, S. A. Plasmonic Nanoantennas: Fundamentals and Their Use in Controlling the Radiative Properties of Nanoemitters. Chem. Rev. 2011, 111, 3888– 3912,  DOI: 10.1021/cr1002672
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    Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters
    Giannini, Vincenzo; Fernandez-Dominguez, Antonio I.; Heck, Susannah C.; Maier, Stefan A.
    Chemical Reviews (Washington, DC, United States) (2011), 111 (6), 3888-3912CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review.
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    Ausman, L. K.; Schatz, G. C. Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons. J. Chem. Phys. 2008, 129, 054704  DOI: 10.1063/1.2961012
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    Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons
    Ausman, Logan K.; Schatz, George C.
    Journal of Chemical Physics (2008), 129 (5), 054704/1-054704/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Calcns. based on the Mie theory are performed to det. the locally enhanced elec. fields due to whispering-gallery mode resonances for dielec. microspheres, with emphasis on electromagnetic hot spots that are located along the wavevector direction on the surface of the sphere. The local elec. field enhancement assocd. with these hot spots is used to det. the surface enhanced Raman scattering enhancement factors for a mol., here treated as a classical dipole, located near the surface of the sphere. Both incident and Raman emission enhancements are calcd. accurately using an extension of the Mie theory that includes interaction of the Raman dipole field with the sphere. The enhancement factors are calcd. for dielec. spheres in vacuum with a refractive index of 1.9 and radii of 5, 10, and 20 μm and for wavelengths that span the visible spectrum. Maximum Raman scattering enhancement factors ∼103-104 are found at locations slightly off the propagation axis when the incident excitation but not the Stokes-shifted radiation is coincident with a whispering-gallery mode resonance. The enhancement factors vary inversely with the resonance width, and this dets. the influence of the mode no. and order on the results. Addnl. calcns. are performed for the case where the Stokes-shifted radiation is on-resonance and Raman enhancement factors as large as 108 are found. These enhancement factors are typically a factor of 102 smaller than would be obtained from |E|4 enhancement ests., as enhancement of the Raman dipole emission is significantly reduced compared to the local field enhancement for micron size particles or larger. Conditions under which single-mol. or few-mol. measurements are feasible are identified. (c) 2008 American Institute of Physics.
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    Foreman, M. R.; Vollmer, F. Level repulsion in hybrid photonic-plasmonic microresonators for enhanced biodetection. Phys. Rev. A 2013, 88, 023831  DOI: 10.1103/PhysRevA.88.023831
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    Level repulsion in hybrid photonic-plasmonic microresonators for enhanced biodetection
    Foreman, Matthew R.; Vollmer, Frank
    Physical Review A: Atomic, Molecular, and Optical Physics (2013), 88 (2-B), 023831/1-023831/6CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
    We theor. analyze photonic-plasmonic coupling between a high-Q whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and red shifts of WGM resonances are shown to arise from crossing of the photonic and plasmonic modes. Level repulsion in the hybrid system is further seen to enable sensitivity enhancements in WGM sensors: maximal when the two resonators are detuned by half the plasmon linewidth. Approx. bounds are given to quantify possible enhancements. Criteria for reactive vs resistive coupling are also established.
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  29. 29
    Thakkar, N.; Rea, M. T.; Smith, K. C.; Heylman, K. D.; Quillin, S. C.; Knapper, K. A.; Horak, E. H.; Masiello, D. J.; Goldsmith, R. H. Sculpting Fano Resonances to Control Photonic-Plasmonic Hybridization. Nano Lett. 2017, 17, 6927– 6934,  DOI: 10.1021/acs.nanolett.7b03332
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    Sculpting Fano Resonances To Control Photonic-Plasmonic Hybridization
    Thakkar, Niket; Rea, Morgan T.; Smith, Kevin C.; Heylman, Kevin D.; Quillin, Steven C.; Knapper, Kassandra A.; Horak, Erik H.; Masiello, David J.; Goldsmith, Randall H.
    Nano Letters (2017), 17 (11), 6927-6934CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Hybrid photonic-plasmonic systems have tremendous potential as versatile platforms for the study and control of nanoscale light-matter interactions since their resp. components have either high-quality factors or low mode vols. Individual metallic nanoparticles deposited on optical microresonators provide an excellent example where ultrahigh-quality optical whispering-gallery modes can be combined with nanoscopic plasmonic mode vols. to maximize the system's photonic performance. Such optimization, however, is difficult in practice because of the inability to easily measure and tune crit. system parameters. In this Letter, we present a general and practical method to det. the coupling strength and tailor the degree of hybridization in composite optical microresonator-plasmonic nanoparticle systems based on exptl. measured absorption spectra. Specifically, we use thermal annealing to control the detuning between a metal nanoparticle's localized surface plasmon resonance and the whispering-gallery modes of an optical microresonator cavity. We demonstrate the ability to sculpt Fano resonance lineshapes in the absorption spectrum and infer system parameters crit. to elucidating the underlying photonic-plasmonic hybridization. We show that including decoherence processes is necessary to capture the evolution of the lineshapes. As a result, thermal annealing allows us to directly tune the degree of hybridization and various hybrid mode quantities such as the quality factor and mode vol. and ultimately maximize the Purcell factor to be 104.
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  30. 30
    Pan, F.; Smith, K. C.; Nguyen, H. L.; Knapper, K. A.; Masiello, D. J.; Goldsmith, R. H. Elucidating Energy Pathways through Simultaneous Measurement of Absorption and Transmission in a Coupled Plasmonic–Photonic Cavity. Nano Lett. 2020, 20, 50– 58,  DOI: 10.1021/acs.nanolett.9b02796
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    30
    Elucidating Energy Pathways through Simultaneous Measurement of Absorption and Transmission in a Coupled Plasmonic-Photonic Cavity
    Pan, Feng; Smith, Kevin C.; Nguyen, Hoang L.; Knapper, Kassandra A.; Masiello, David J.; Goldsmith, Randall H.
    Nano Letters (2020), 20 (1), 50-58CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Control of light-matter interactions is central to numerous advances in quantum communication, information, and sensing. The relative ease with which interactions can be tailored in coupled plasmonic-photonic systems makes them ideal candidates for investigation. To exert control over the interaction between photons and plasmons, it is essential to identify the underlying energy pathways which influence the system's dynamics and det. the crit. system parameters, such as the coupling strength and dissipation rates. However, in coupled systems which dissipate energy through multiple competing pathways, simultaneously resolving all parameters from a single expt. is challenging as typical observables such as absorption and scattering each probe only a particular path. In this work, we simultaneously measure both photothermal absorption and two-sided optical transmission in a coupled plasmonic-photonic resonator consisting of plasmonic gold nanorods deposited on a toroidal whispering-gallery-mode optical microresonator. We then present an anal. model which predicts and explains the distinct line shapes obsd. and quantifies the contribution of each system parameter. By combining this model with expt., we ext. all system parameters with a dynamic range spanning 9 orders of magnitude. Our combined approach provides a full description of plasmonic-photonic energy dynamics in a weakly coupled optical system, a necessary step for future applications that rely on tunability of dissipation and coupling.
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    Frimmer, M.; Koenderink, A. F. Superemitters in hybrid photonic systems: A simple lumping rule for the local density of optical states and its breakdown at the unitary limit. Phys. Rev. B 2012, 86, 235428  DOI: 10.1103/PhysRevB.86.235428
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    31
    Superemitters in hybrid photonic systems: a simple lumping rule for the local density of optical states and its breakdown at the unitary limit
    Frimmer, Martin; Koenderink, A. Femius
    Physical Review B: Condensed Matter and Materials Physics (2012), 86 (23), 235428/1-235428/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We theor. investigate how the enhancement of the radiative decay rate of a spontaneous emitter provided by coupling to an optical antenna is modified when this "superemitter" is introduced into a complex photonic environment that provides an enhanced local d. of optical states (LDOS) itself, such as a microcavity or stratified medium. We show that photonic environments with increased LDOS further boost the performance of antennas that scatter weakly, for which a simple multiplicative LDOS lumping rule holds. In contrast, enhancements provided by antennas close to the unitary limit, i.e., close to the limit of maximally possible scattering strength, are strongly reduced by an enhanced LDOS of the environment. Thus, we identify multiple scattering in hybrid photonic systems as a powerful mechanism for LDOS engineering.
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    Kamandar Dezfouli, M.; Gordon, R.; Hughes, S. Modal theory of modified spontaneous emission of a quantum emitter in a hybrid plasmonic photonic-crystal cavity system. Phys. Rev. A 2017, 95, 013846  DOI: 10.1103/PhysRevA.95.013846
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    Barth, M.; Schietinger, S.; Fischer, S.; Becker, J.; Nüsse, N.; Aichele, T.; Löchel, B.; Sönnichsen, C.; Benson, O. Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling. Nano Lett. 2010, 10, 891– 895,  DOI: 10.1021/nl903555u
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    Nanoassembled Plasmonic-Photonic Hybrid Cavity for Tailored Light-Matter Coupling
    Barth, Michael; Schietinger, Stefan; Fischer, Sabine; Becker, Jan; Nuesse, Nils; Aichele, Thomas; Loechel, Bernd; Soennichsen, Carsten; Benson, Oliver
    Nano Letters (2010), 10 (3), 891-895CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    The authors propose and demonstrate a hybrid cavity system in which metal nanoparticles are evanescently coupled to a dielec. photonic crystal cavity using a nanoassembly method. While the metal constituents lead to strongly localized fields, optical feedback is provided by the surrounding photonic crystal structure. The combined effect of plasmonic field enhancement and high quality factor (Q ≈ 900) opens new routes for the control of light-matter interaction at the nanoscale.
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    Gurlek, B.; Sandoghdar, V.; Martín-Cano, D. Manipulation of Quenching in Nanoantenna-Emitter Systems Enabled by External Detuned Cavities: A Path to Enhance Strong-Coupling. ACS Photonics 2018, 5, 456– 461,  DOI: 10.1021/acsphotonics.7b00953
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    Manipulation of Quenching in Nanoantenna-Emitter Systems Enabled by External Detuned Cavities: A Path to Enhance Strong-Coupling
    Gurlek, Burak; Sandoghdar, Vahid; Martin-Cano, Diego
    ACS Photonics (2018), 5 (2), 456-461CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    A broadband Fabry-Perot microcavity can assist an emitter coupled to an off-resonant plasmonic nanoantenna to inhibit the nonradiative channels that affect the quenching of fluorescence. The interference mechanism that creates the necessary enhanced couplings and bandwidth narrowing of the hybrid resonance are identified, and it can assist entering into the strong coupling regime. The results provide new possibilities for improving the efficiency of solid-state emitters and accessing diverse realms of photophysics with hybrid structures that can be fabricated using existing technols.
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    Palstra, I. M.; Doeleman, H. M.; Koenderink, A. F. Hybrid cavity-antenna systems for quantum optics outside the cryostat?. Nanophotonics 2019, 8, 1513– 1531,  DOI: 10.1515/nanoph-2019-0062
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    Hybrid cavity-antenna systems for quantum optics outside the cryostat?
    Palstra, Isabelle M.; Doeleman, Hugo M.; Koenderink, A. Femius
    Nanophotonics (2019), 8 (9), 1513-1531CODEN: NANOLP; ISSN:2192-8614. (Walter de Gruyter GmbH)
    Hybrid cavity-antenna systems have been proposed to combine the sub-wavelength light confinement of plasmonic antennas with microcavity quality factors Q. Here, we examine what confinement and Q can be reached in these hybrid systems, and we address their merits for various applications in classical and quantum optics. Specifically, we investigate their applicability for quantum-optical applications at noncryogenic temps. To this end we first derive design rules for hybrid resonances from a simple anal. model. These rules are benchmarked against full-wave simulations of hybrids composed of state-of-the-art nanobeam cavities and plasmonic-dimer gap antennas. We find that hybrids can outperform the plasmonic and cavity constituents in terms of Purcell factor, and addnl. offer freedom to reach any Q at a similar Purcell factor. We discuss how these metrics are highly advantageous for a high Purcell factor, yet weak-coupling applications, such as bright sources of indistinguishable single photons. The challenges for room-temp. strong coupling, however, are far more daunting: the extremely high dephasing of emitters implies that little benefit can be achieved from trading confinement against a higher Q, as done in hybrids. An attractive alternative could be strong coupling at liq. nitrogen temp., where emitter dephasing is lower and this trade-off can alleviate the stringent fabrication demands required for antenna strong coupling. For few-emitter strong-coupling, high-speed and low-power coherent or incoherent light sources, particle sensing and vibrational spectroscopy, hybrids provide the unique benefit of very high local optical d. of states, tight plasmonic confinement, yet microcavity Q.
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    Doeleman, H. M.; Dieleman, C. D.; Mennes, C.; Ehrler, B.; Koenderink, A. F. Observation of Cooperative Purcell Enhancements in Antenna-Cavity Hybrids. ACS Nano 2020, 14, 12027– 12036,  DOI: 10.1021/acsnano.0c05233
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    Observation of Cooperative Purcell Enhancements in Antenna-Cavity Hybrids
    Doeleman, Hugo M.; Dieleman, Christian D.; Mennes, Christiaan; Ehrler, Bruno; Koenderink, A. Femius
    ACS Nano (2020), 14 (9), 12027-12036CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Localizing light to nanoscale vols. through nanoscale resonators that are low loss and precisely tailored in spectrum to properties of matter is crucial for classical and quantum light sources, cavity QED, mol. spectroscopy, and many other applications. To date, two opposite strategies have been identified: to use either plasmonics with deep subwavelength confinement yet high loss and very poor spectral control or instead microcavities with exquisite quality factors yet poor confinement. In this work we realize hybrid plasmonic-photonic resonators that enhance the emission of single quantum dots, profiting from both plasmonic confinement and microcavity quality factors. Our expts. directly demonstrate how cavity and antenna jointly realize large cooperative Purcell enhancements through interferences. These can be controlled to engineer arbitrary Fano lineshapes in the local d. of optical states.
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    Dezfouli, M. K.; Gordon, R.; Hughes, S. Molecular Optomechanics in the Anharmonic Cavity-QED Regime Using Hybrid Metal-Dielectric Cavity Modes. ACS Photonics 2019, 6, 1400– 1408,  DOI: 10.1021/acsphotonics.8b01091
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    Molecular Optomechanics in the Anharmonic Cavity-QED Regime Using Hybrid Metal-Dielectric Cavity Modes
    Dezfouli, Mohsen Kamandar; Gordon, Reuven; Hughes, Stephen
    ACS Photonics (2019), 6 (6), 1400-1408CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Using carefully designed hybrid metal-dielec. resonators, the authors mol. optomechanics was studied in the strong coupling regime (g2/ωm>κ), which manifests in anharmonic emission lines in the sideband-resolved region of the cavity-emitted spectrum (κ<ωm). This optomech. strong coupling regime is enabled through a metal-dielec. cavity system that yields not only deep sub-wavelength plasmonic confinement, but also dielec.-like confinement times that are >2 orders of magnitude larger than those from typical localized plasmon modes. The classical mode parameters are quantified using quasinormal mode theory, and the quantum dynamics are computed using both std. and generalized quantum master equations. These hybrid metal-dielec. cavity modes enable study of new avenues of quantum plasmonics for single mol. Raman scattering.
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    Ameling, R.; Giessen, H. Microcavity plasmonics: strong coupling of photonic cavities and plasmons. Laser Photonics Rev. 2013, 7, 141– 169,  DOI: 10.1002/lpor.201100041
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    Microcavity plasmonics: strong coupling of photonic cavities and plasmons
    Ameling, Ralf; Giessen, Harald
    Laser & Photonics Reviews (2013), 7 (2), 141-169CODEN: LPRAB8; ISSN:1863-8880. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. The understanding of light-matter interactions at the nanoscale lays the groundwork for many future technologies, applications and materials. The scope of this article is the investigation of coupled photonic-plasmonic systems consisting of a combination of photonic microcavities and metallic nanostructures. In such systems, it is possible to observe an exceptionally strong coupling between electromagnetic light modes of a resonator and collective electron oscillations (plasmons) in the metal. Furthermore, the results have shown that coupled photonic-plasmonic structures possess a considerably higher sensitivity to changes in their environment than conventional localized plasmon sensors due to a plasmon excitation phase shift that depends on the environment.
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    Soltani, S.; Diep, V. M.; Zeto, R.; Armani, A. M. Stimulated Anti-Stokes Raman Emission Generated by Gold Nanorod Coated Optical Resonators. ACS Photonics 2018, 5, 3550– 3556,  DOI: 10.1021/acsphotonics.8b00296
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    Stimulated Anti-Stokes Raman Emission Generated by Gold Nanorod Coated Optical Resonators
    Soltani, Soheil; Diep, Vinh M.; Zeto, Rene; Armani, Andrea M.
    ACS Photonics (2018), 5 (9), 3550-3556CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Plasmonic nanomaterials and nanostructured substrates have made a significant impact in sensing and imaging due to their ability to improve optical field confinement at interfaces. This improved confinement increases the optical field intensity, enabling numerous nonlinear effects to be revealed. One challenge is effectively coupling light into and out of the plasmonic nanomaterial. One approach is to directly integrate the plasmonic nanomaterials onto the surface of light emitting optical devices. The highly nonlinear complex of org. small mol. functionalized Au nanorods is coated on the surface of optical resonators. The evanescent tail of the optical field circulating inside the resonator directly interacts with the nanoparticle complex, creating a hybridized plasmon-whispering gallery mode. Due to the strong field localization by the nanorods and the large circulating power within the resonator, Stimulated Anti-Stokes Raman Scattering is generated with only 14 mW of input power, which is a 4-fold redn. as compared to previous work.
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    Liu, W.; Chen, Y.-L.; Tang, S.-J.; Vollmer, F.; Xiao, Y.-F. Nonlinear Sensing with Whispering-Gallery Mode Microcavities: From Label-Free Detection to Spectral Fingerprinting. Nano Lett. 2021, 21, 1566– 1575,  DOI: 10.1021/acs.nanolett.0c04090
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    Nonlinear Sensing with Whispering-Gallery Mode Microcavities: From Label-Free Detection to Spectral Fingerprinting
    Liu, Wenjing; Chen, You-Ling; Tang, Shui-Jing; Vollmer, Frank; Xiao, Yun-Feng
    Nano Letters (2021), 21 (4), 1566-1575CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    A review. Optical microresonators have attracted intense interests in highly sensitive mol. detection and optical precision measurement in the past decades. In particular, the combination of a high quality factor with a small mode vol. significantly enhances the nonlinear light-matter interaction in whispering-gallery mode (WGM) microresonators, which greatly boost nonlinear optical sensing applications. Nonlinear WGM microsensors not only allow for label-free detection of mols. with an ultrahigh sensitivity but also support new functionalities in sensing such as the specific spectral fingerprinting of mols. with frequency conversion involved. Here, we review the mechanisms, sensing modalities, and recent progresses of nonlinear optical sensors along with a brief outlook on the possible future research directions of this rapidly advancing field.
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    Peyskens, F.; Dhakal, A.; Van Dorpe, P.; Le Thomas, N.; Baets, R. Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform. ACS Photonics 2016, 3, 102– 108,  DOI: 10.1021/acsphotonics.5b00487
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    Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform
    Peyskens, Frederic; Dhakal, Ashim; Van Dorpe, Pol; Le Thomas, Nicolas; Baets, Roel
    ACS Photonics (2016), 3 (1), 102-108CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    We demonstrate the generation of Surface Enhanced Raman Spectroscopy (SERS) signals from integrated bowtie antennas, excited and collected by the fundamental TE mode of a single mode silicon nitride waveguide. Due to the integrated nature of this particular single mode SERS probe one can rigorously quantify the complete enhancement process. The Stokes power, generated by a 4-nitrothiophenol-coated antenna and collected into the fundamental TE mode, exhibits an 8 × 106 enhancement compared to the free space Raman scattering of a 4-nitrothiophenol mol. Furthermore, we present an anal. model which identifies the relevant design parameters and figure of merit for this new SERS-platform. An excellent correspondence is obtained between the theor. predicted and exptl. obsd. abs. Raman power. This work paves the way toward a new class of fully integrated lab-on-a-chip systems where the single mode SERS probe can be combined with other photonic, fluidic, or biol. functionalities.
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    Doeleman, H. M.; Verhagen, E.; Koenderink, A. F. Antenna-Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth. ACS Photonics 2016, 3, 1943– 1951,  DOI: 10.1021/acsphotonics.6b00453
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    Antenna-Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth
    Doeleman, Hugo M.; Verhagen, Ewold; Koenderink, A. Femius
    ACS Photonics (2016), 3 (10), 1943-1951CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Strong interaction between light and a single quantum emitter is essential to a great no. of applications, including single photon sources. Microcavities and plasmonic antennas have been used frequently to enhance these interactions through the Purcell effect. Both can provide large emission enhancements: the cavity typically through long photon lifetimes (high Q), and the antenna mostly through strong field enhancement (low mode vol. V). In this work, we demonstrate that a hybrid system, which combines a cavity and a dipolar antenna, can achieve stronger emission enhancements than the cavity or antenna alone. We show that these systems can in fact break the fundamental limit on single antenna enhancement. Addnl., hybrid systems can be used as a versatile platform to tune the bandwidth of enhancement to any desired value between that of the cavity and the antenna, while simultaneously boosting emission enhancement. Our fully self-consistent anal. model allows to identify the underlying mechanisms of boosted emission enhancement in hybrid systems, which include radiation damping and constructive interference between multiple-scattering paths. Moreover, we find excellent agreement between strongly boosted enhancement spectra from our anal. model and from finite-element simulations on a realistic cavity-antenna system. Finally, we demonstrate that hybrid systems can simultaneously boost emission enhancement and maintain a near-unity outcoupling efficiency into a single cavity decay channel, such as a waveguide.
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    Barker, A. S.; Loudon, R. Response Functions in the Theory of Raman Scattering by Vibrational and Polariton Modes in Dielectric Crystals. Rev. Mod. Phys. 1972, 44, 18– 47,  DOI: 10.1103/RevModPhys.44.18
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    Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals
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    Reviews of Modern Physics (1972), 44 (1), 18-47CODEN: RMPHAT; ISSN:0034-6861.
    An introduction is given to the theory of inelastic light scattering by polaritons in dielec. crystals. The treatment is based on a simple 2-oscillator model which represents the ionic and electronic motions of a crystal. The model contains a 3rd-order anharmonicity which allows an incident laser beam to mix with the oscillator fluctuations and produce scattered light of frequency different from the incident frequency. The magnitude of the oscillator fluctuations is detd. by an application of the Nyquist or fluctuation-dissipation theorem, by using the response functions of the oscillators for externally applied forces. The simple model gives results for light scattering cross sections which agree with more rigorous derivations in the existing literature. The response function approach is generalized to apply to crystals having many ionic resonances and of uniaxial or orthorhombic structure. The general formulas reduce in appropriate special cases to results already published. Exptl. and theoretical work on light scattering by polaritons and by pure phonons is reviewed in the context of both the 2-oscillator model and the general theory. Particular attention is given to resonance scattering in an attempt to achieve consistency between the differing theoretical treatments in the literature. The subject matter of the review overlaps some topics in nonlinear optics, and contact is made with the theories of the electrooptic effect and stimulated Raman scattering.
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    Fano resonances in photonics
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    Nature Photonics (2017), 11 (9), 543-554CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
    Rapid progress in photonics and nanotechnol. brings many examples of resonant optical phenomena assocd. with the physics of Fano resonances, with applications in optical switching and sensing. For successful design of photonic devices, it is important to gain deep insight into different resonant phenomena and understand their connection. Here, we review a broad range of resonant electromagnetic effects by using two effective coupled oscillators, including the Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity-time symmetry breaking. We discuss how to introduce the Fano parameter for describing a transition between two seemingly different spectroscopic signatures assocd. with asym. Fano and sym. Lorentzian shapes. We also review the recent results on Fano resonances in dielec. nanostructures and metasurfaces.
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    Xomalis, A.; Chikkaraddy, R.; Oksenberg, E.; Shlesinger, I.; Huang, J.; Garnett, E. C.; Koenderink, A. F.; Baumberg, J. J. Controlling Optically Driven Atomic Migration Using Crystal-Facet Control in Plasmonic Nanocavities. ACS Nano 2020, 14, 10562– 10568,  DOI: 10.1021/acsnano.0c04600
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    Controlling Optically Driven Atomic Migration Using Crystal-Facet Control in Plasmonic Nanocavities
    Xomalis, Angelos; Chikkaraddy, Rohit; Oksenberg, Eitan; Shlesinger, Ilan; Huang, Junyang; Garnett, Erik C.; Koenderink, A. Femius; Baumberg, Jeremy J.
    ACS Nano (2020), 14 (8), 10562-10568CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Plasmonic nanoconstructs are widely exploited to confine light for applications ranging from quantum emitters to medical imaging and biosensing. However, accessing extreme near-field confinement using the surfaces of metallic nanoparticles often induces permanent structural changes from light, even at low intensities. Here, we report a robust and simple technique to exploit crystal facets and their at. boundaries to prevent the hopping of atoms along and between facet planes. Avoiding X-ray or electron microscopy techniques that perturb these at. restructurings, we use elastic and inelastic light scattering to resolve the influence of crystal habit. A clear increase in stability is found for {100} facets with steep inter-facet angles, compared to multiple at. steps and shallow facet curvature on spherical nanoparticles. Avoiding at. hopping allows Raman scattering on mols. with low Raman cross-section while circumventing effects of charging and adatom binding, even over long measurement times. These nanoconstructs allow the optical probing of dynamic reconstruction in nanoscale surface science, photocatalysis, and mol. electronics.
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    A review. Optical microcavities confine light to small vols. by resonant recirculation. Devices based on optical microcavities are already indispensable for a wide range of applications and studies. For example, microcavities made of active III-V semiconductor materials control laser emission spectra to enable long-distance transmission of data over optical fibers; they also ensure narrow spot-size laser read/write beams in CD and DVD players. In quantum optical devices, microcavities can coax atoms or quantum dots to emit spontaneous photons in a desired direction or can provide an environment where dissipative mechanisms such as spontaneous emission are overcome so that quantum entanglement of radiation and matter is possible. Applications of these remarkable devices are as diverse as their geometrical and resonant properties.
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    Bain, Colin D.; Biebuyck, Hans A.; Whitesides, George M.
    Langmuir (1989), 5 (3), 723-7CODEN: LANGD5; ISSN:0743-7463.
    Ordered, org. monolayers were formed on Au slides by adsorption from EtOH of HS(CH2)10CH2OH, HS(CH2)10CH3, [S(CH2)10CH2OH]2, [S(CH2)10CH3]2, and binary mixts. of these mols. in which 1 component was terminated by a hydrophobic Me group and 1 by a hydrophilic alc. group. The compns. of the monolayers were detd. by XPS. Wettability was used as a probe of the chem. compn. and structure of the surface of the monolayer. When monolayers were formed in solns. contg. mixts. of a thiol and a disulfide, adsorption of the thiol was strongly preferred (∼75:1). The advancing contact angles of water and hexadecane on monolayers formed from solns. contg. mixts. of 2 thiols, a thiol and a disulfide, or 2 disulfides depend on the proportion of OH-terminated chains in the monolayer and are largely independent of the nature of the precursor species. This observation suggests that both thiols and disulfides give rise to the same chem. species (probably a thiolate) on the surface. This model is supported by the observation by XPS of indistinguishable S(2p) signals from monolayers derived from thiols and disulfides.
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    Physical Review A (2018), 98 (4), 043615CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
    We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly dets. the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.
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    Kapfinger, S.; Reichert, T.; Lichtmannecker, S.; Müller, K.; Finley, J. J.; Wixforth, A.; Kaniber, M.; Krenner, H. J. Dynamic Acousto-Optic Control of a Strongly Coupled Photonic Molecule. Nat. Commun. 2015, 6, 8540  DOI: 10.1038/ncomms9540
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    Nature Communications (2015), 6 (), 8540CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Strongly confined photonic modes can couple to quantum emitters and mech. excitations. To harness the full potential in quantum photonic circuits, interactions between different constituents have to be precisely and dynamically controlled. Here, a prototypical coupled element, a photonic mol. defined in a photonic crystal membrane, is controlled by a radio frequency surface acoustic wave. The sound wave is tailored to deliberately switch on and off the bond of the photonic mol. on sub-nanosecond timescales. In time-resolved expts., the acousto-optically controllable coupling is directly obsd. as clear anticrossings between the two nanophotonic modes. The coupling strength is detd. directly from the exptl. data. Both the time dependence of the tuning and the inter-cavity coupling strength are found to be in excellent agreement with numerical calcns. The demonstrated mech. technique can be directly applied for dynamic quantum gate operations in state-of-the-art-coupled nanophotonic, quantum cavity electrodynamic and optomech. systems.
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    Physical Review Letters (2010), 104 (8), 083901/1-083901/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The phonon analog of an optical laser has long been a subject of interest. The authors demonstrate a compd. microcavity system, coupled to a radiofrequency mech. mode, that operates in close analogy to a two-level laser system. An inversion produces gain, causing phonon laser action above a pump power threshold of ∼7 μW. The device features a continuously tunable gain spectrum to selectively amplify mech. modes from radio frequency to microwave rates. Viewed as a Brillouin process, the system accesses a regime in which the phonon plays what has traditionally been the role of the Stokes wave. For this reason, it should also be possible to controllably switch between phonon and photon laser regimes. Cooling of the mech. mode is also possible.
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    Jing, H.; Özdemir, S. K.; Lü, X.-Y.; Zhang, J.; Yang, L.; Nori, F. PT-Symmetric Phonon Laser. Phys. Rev. Lett. 2014, 113, 053604  DOI: 10.1103/PhysRevLett.113.053604
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    PT-symmetric phonon laser
    Jing, Hui; Ozdemir, S. K.; Lu, Xin-You; Zhang, Jing; Yang, Lan; Nori, Franco
    Physical Review Letters (2014), 113 (5), 053604CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    By exploiting recent developments assocd. with coupled microcavities, we introduce the concept of PT-sym. phonon laser with balanced gain and loss. This is accomplished by introducing gain to one of the microcavities such that it balances the passive loss of the other. In the vicinity of the gain-loss balance, a strong nonlinear relation emerges between the intracavity-photon intensity and the input power. This then leads to a giant enhancement of both optical pressure and mech. gain, resulting in a highly efficient phonon-lasing action. These results provide a promising approach for manipulating optomech. systems through PT-sym. concepts. Potential applications range from enhancing mech. cooling to designing phonon-laser amplifiers.
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This article is cited by 4 publications.

  1. Bisweswar Patra, Bijesh Kafle, Terefe G. Habteyes. Molecular Optomechanics Induced Hybrid Properties in Soft Materials Filled Plasmonic Nanocavities. Nano Letters 2023, 23 (11) , 5108-5115. https://doi.org/10.1021/acs.nanolett.3c01035
  2. Ilan Shlesinger, Isabelle M. Palstra, A. Femius Koenderink. Integrated Sideband-Resolved SERS with a Dimer on a Nanobeam Hybrid. Physical Review Letters 2023, 130 (1) https://doi.org/10.1103/PhysRevLett.130.016901
  3. Qiaohua Wu, Yingqiu Zhang, Desheng Qu, Chunlei Li. Independently tunable triple Fano resonances in plasmonic waveguide structure and its applications for sensing. Journal of Nanophotonics 2022, 16 (03) https://doi.org/10.1117/1.JNP.16.036008
  4. Xiao Xiong, Yun-Feng Xiao. Hybrid plasmonic-photonic microcavity for enhanced light-matter interaction. Science Bulletin 2022, 67 (12) , 1205-1208. https://doi.org/10.1016/j.scib.2022.04.021
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  • Abstract

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    Figure 1

    Figure 1. Raman scattering enhanced by a hybrid dielectric–plasmonic resonator. Top: sketch of a typical system: the spectrally narrow modes of a dielectric cavity hybridize with a plasmonic antenna resulting in high-Q small-mode-volume resonances, ideal for sideband resolved molecular optomechanics. Light can couple in and out through different ports such as the free-space or waveguides. Bottom: the hybrid system can be used to enhance both the laser pump and Raman sidebands, even in the sideband resolved regime, where the linewidth of the optical resonances are narrower than the mechanical frequency Ωm.

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    Figure 2

    Figure 2. Raman spectrum enhanced by an antenna (a) as a function of the laser frequency, normalized by the Stokes emission peak of the molecules in air SrefStokes(ωL). The cross-cuts at the dashed blue and green lines correspond to (b) and (c). (b) Raman spectrum at the maximum enhancement and (c) antenna enhancement at the Stokes sideband as a function of the laser frequency. (d) Raman spectrum of the bare antenna Santbare, normalized by the Raman emission of the molecules in air Sref showing the antenna SERS enhancement as a function of the laser and detected frequencies. It is equal to the product of a pump enhancement term (e) and of a collected LDOS enhancement term (f). The case of a hybrid antenna–cavity resonator is given in (g)–(l), exhibiting narrow Fano resonances both in the Raman spectrum and in the pump and LDOS enhancements. See text for parameters.

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    Figure 3

    Figure 3. Stokes enhancement for the four different combinations of input–output as depicted on the sketches. Each Stokes enhancement (iii) is obtained as the product of the pump enhancement at ωL (i) and the collected LDOS at ωD = ωL – Ωm (ii) for the given input and output, respectively. The bare antenna response is plotted in the dashed curve in panel (a). The parameters are the same as in Figure 2.

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    Figure 4

    Figure 4. Influence of the cavity–antenna detuning Δca on the Stokes enhancement for free-space input/output (a) and free-space input and waveguide output (c). The antenna frequency is fixed at ωa/(2π) = 460 THz, and the cavity frequency is scanned around ωa – Ωm in steps of 16κ. The maximum Stokes enhancement for each detuning is shown in (b) and (d) for the two collection cases, with the colored crosses corresponding to the respective colored plots in (a) and (c).

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    Figure 5

    Figure 5. Maximum achievable pump enhancement (a, b) and LDOSC (c, d) as a function of the cavity quality factor Qc for both input and output configurations; (a) and (c) are given for a fixed-mode volume Vc = 10λ3, whereas (b) and (d) are given for a constant-cavity Purcell factor Qc/Vc. The antenna frequency is ωa/(2π) = 460 THz, and the cavity frequency is fixed at ωc = ωa – Ωm. The horizontal dotted line corresponds to the free-space case with only the bare antenna.

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    Figure 6

    Figure 6. Anti-Stokes enhancement for different cavity–antenna detunings. The antenna is now red-detuned (ωa = 400 THz) to enhance the pump, and the cavity frequency is scanned around the anti-Stokes sideband (ωa + Ωm) in steps of 16κ. The input is in free space, and the collection is either in free space (a) or in the waveguide (b).

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    Figure 7

    Figure 7. Stokes enhancement with a two-mode cavity and an antenna hybrid. The antenna is blue-detuned ωa/(2π) = 460 THz with respect to both cavity modes. The first cavity mode serves as pump enhancement at ωP/(2π) = 415 THz, and the Stokes sideband emission is enhanced by the second cavity mode, which is scanned around ωP – Ωm. We compare the cases with free-space-only (a) or waveguide-only (b) input and output. The Stokes enhancement is again the product of a pump enhancement factor and the collected LDOS. The inset in (b) shows a close-up of the best Raman enhancements close to ωL = ωP.

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    Figure 8

    Figure 8. (a) Low-noise, integrated, IR-to-visible transduction using reservoir engineering. Using multiple cavity modes, one can selectively enhance the up-converted anti-Stokes while suppressing unwanted back-action noise. (b) Anti-Stokes enhancement with a two-mode cavity and an antenna hybrid. Parameters are the same as in Figure 7, with the laser now pumping the redder cavity. The red solid line corresponds to collection through the waveguide (fully integrated system), while the dashed blue line is for a collection through free space. (c) Integrated behavior: fraction of collected light into the waveguide (WG), reaching values up to 80% due to the Fano dip in the response function of the hybridized antenna.

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  • References

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      Zhang, Yuan; Esteban, Ruben; Boto, Roberto A.; Urbieta, Mattin; Arrieta, Xabier; Shan, ChongXin; Li, Shuzhou; Baumberg, Jeremy J.; Aizpurua, Javier
      Nanoscale (2021), 13 (3), 1938-1954CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
      The description of surface-enhanced Raman scattering (SERS) as a mol. optomech. process has provided new insights into the vibrational dynamics and nonlinearities of this inelastic scattering process. In earlier studies, mol. vibrations have typically been assumed to couple with a single plasmonic mode of a metallic nanostructure, ignoring the complexity of the plasmonic response in many configurations of practical interest such as in metallic nanojunctions. By describing the plasmonic fields as a continuum, we demonstrate here the importance of considering the full plasmonic response to properly address the mol.-cavity optomech. interaction. We apply the continuum-field model to calc. the Raman signal from a single mol. in a plasmonic nanocavity formed by a nanoparticle-on-a-mirror configuration, and compare the results of optomech. parameters, vibrational populations, and Stokes and anti-Stokes signals of the continuum-field model with those obtained from the single-mode model. Moreover, Raman linewidths, lineshifts, vibrational populations, and parametric instabilities are found to be sensitive to the energy of the mol. vibrational modes. The implications of adopting the continuum-field model to describe the plasmonic cavity response in mol. optomechanics are relevant in many other nanoantenna and nanocavity configurations commonly used to enhance SERS.
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    12. 12
      Roelli, P.; Galland, C.; Piro, N.; Kippenberg, T. J. Molecular cavity optomechanics as a theory of plasmon-enhanced Raman scattering. Nat. Nanotechnol. 2016, 11, 164– 169,  DOI: 10.1038/nnano.2015.264
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      12
      Molecular cavity optomechanics as a theory of plasmon-enhanced Raman scattering
      Roelli, Philippe; Galland, Christophe; Piro, Nicolas; Kippenberg, Tobias J.
      Nature Nanotechnology (2016), 11 (2), 164-169CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
      The exceptional enhancement of Raman scattering by localized plasmonic resonances in the near field of metallic nanoparticles, surfaces or tips (SERS, TERS) has enabled spectroscopic fingerprinting down to the single mol. level. The conventional explanation attributes the enhancement to the subwavelength confinement of the electromagnetic field near nanoantennas. Here, we introduce a new model that also accounts for the dynamical nature of the plasmon-mol. interaction. We thereby reveal an enhancement mechanism not considered before: dynamical backaction amplification of mol. vibrations. We first map the system onto the canonical Hamiltonian of cavity optomechanics, in which the mol. vibration and the plasmon are parametrically coupled. We express the vacuum optomech. coupling rate for individual mols. in plasmonic 'hot-spots' in terms of the vibrational mode's Raman activity and find it to be orders of magnitude larger than for microfabricated optomech. systems. Remarkably, the frequency of commonly studied mol. vibrations can be comparable to or larger than the plasmon's decay rate. Together, these considerations predict that an excitation laser blue-detuned from the plasmon resonance can parametrically amplify the mol. vibration, leading to a nonlinear enhancement of Raman emission that is not predicted by the conventional theory. Our optomech. approach recovers known results, provides a quant. framework for the calcn. of cross-sections, and enables the design of novel systems that leverage dynamical backaction to achieve addnl., mode-selective enhancements. It also provides a quantum mech. framework to analyze plasmon-vibrational interactions in terms of mol. quantum optomechanics.
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    13. 13
      Schmidt, M. K.; Esteban, R.; González-Tudela, A.; Giedke, G.; Aizpurua, J. Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities. ACS Nano 2016, 10, 6291– 6298,  DOI: 10.1021/acsnano.6b02484
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      13
      Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities
      Schmidt, Mikolaj K.; Esteban, Ruben; Gonzalez-Tudela, Alejandro; Giedke, Geza; Aizpurua, Javier
      ACS Nano (2016), 10 (6), 6291-6298CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Plasmon-enhanced Raman scattering can push single-mol. vibrational spectroscopy beyond a regime addressable by classical electrodynamics. The authors employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and mol. vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, the authors predict the onset of phonon-stimulated Raman scattering and a counterintuitive dependence of the anti-Stokes emission on the frequency of excitation. Further this QED framework opens a venue to analyze the correlations of photons emitted from a plasmonic cavity.
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    14. 14
      Schmidt, M. K.; Esteban, R.; Benz, F.; Baumberg, J. J.; Aizpurua, J. Linking classical and molecular optomechanics descriptions of SERS. Faraday Discuss. 2017, 205, 31– 65,  DOI: 10.1039/C7FD00145B
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      14
      Linking classical and molecular optomechanics descriptions of SERS
      Schmidt, Mikolaj K.; Esteban, Ruben; Benz, Felix; Baumberg, Jeremy J.; Aizpurua, Javier
      Faraday Discussions (2017), 205 (Surface Enhanced Raman Scattering--SERS), 31-65CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
      The surface-enhanced Raman scattering (SERS) of mol. species in plasmonic cavities can be described as an optomech. process where plasmons constitute an optical cavity of reduced effective mode vol. which effectively couples to the vibrations of the mols. An optomech. Hamiltonian can address the full quantum dynamics of the system, including the phonon population build-up, the vibrational pumping regime, and the Stokes-anti-Stokes correlations of the photons emitted. Here we describe in detail two different levels of approxn. to the methodol. soln. of the optomech. Hamiltonian of a generic SERS configuration, and compare the results of each model in light of recent expts. Furthermore, a phenomenol. semi-classical approach based on a rate equation of the phonon population is demonstrated to be formally equiv. to that obtained from the full quantum optomech. approach. The evolution of the Raman signal with laser intensity (thermal, vibrational pumping and instability regimes) is accurately addressed when this phenomenol. semi-classical approach is properly extended to account for the anti-Stokes process. The formal equivalence between semi-classical and mol. optomechanics descriptions allows us to describe the vibrational pumping regime of SERS through the classical cross sections which characterize a nanosystem, thus setting a roadmap to describing mol. optomech. effects in a variety of exptl. situations.
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    15. 15
      Maher, R. C.; Galloway, C. M.; Le Ru, E. C.; Cohen, L. F.; Etchegoin, P. G. Vibrational pumping in surface enhanced Raman scattering (SERS). Chem. Soc. Rev. 2008, 37, 965– 979,  DOI: 10.1039/b707870f
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      15
      Vibrational pumping in surface enhanced Raman scattering (SERS)
      Maher, R. C.; Galloway, C. M.; Le Ru, E. C.; Cohen, L. F.; Etchegoin, P. G.
      Chemical Society Reviews (2008), 37 (5), 965-979CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. In this tutorial review, the underlying principles of vibrational pumping in surface enhanced Raman scattering (SERS) are summarized and explained within the framework of their historical development. Some state-of-the-art results in the field are also presented, with the aim of giving an overview on what was established at this stage, as well as hinting at areas where future developments might take place.
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    16. 16
      Zhang, Y.; Aizpurua, J.; Esteban, R. Optomechanical Collective Effects in Surface-Enhanced Raman Scattering from Many Molecules. ACS Photonics 2020, 7, 1676– 1688,  DOI: 10.1021/acsphotonics.0c00032
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      16
      Optomechanical Collective Effects in Surface-Enhanced Raman Scattering from Many Molecules
      Zhang, Yuan; Aizpurua, Javier; Esteban, Ruben
      ACS Photonics (2020), 7 (7), 1676-1688CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      The interaction between mols. is commonly ignored in surface-enhanced Raman scattering (SERS). Under this assumption, the total SERS signal is described as the sum of the individual contributions of each mol. treated independently. We adopt here an optomech. description of SERS within a cavity quantum electrodynamics framework to study how collective effects emerge from the quantum correlations of distinct mols. We derive anal. expressions for identical mols. and implement numerical simulations to analyze two types of collective phenomena: (i) a decrease of the laser intensity threshold to observe strong nonlinearities as the no. of mols. increases, within very intense illumination, and (ii) identification of superradiance in the SERS signal, namely a quadratic scaling with the no. of mols. The laser intensity required to observe the latter in the anti-Stokes scattering is relatively moderate, which makes it particularly accessible to expts. We treat the system on the basis of the individual mols. and demonstrate that for ideal systems with identical mols. this approach is equiv. to a description based on collective modes. The basis of individual mols. also allows for describing in a straightforward manner more general systems where the mols. might have different vibrational properties or suffer from pure-dephasing processes. Our results show that the collective phenomena can survive in the presence of the homogeneous and inhomogeneous broadening that might influence exptl. results.
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    17. 17
      Benz, F.; Schmidt, M. K.; Dreismann, A.; Chikkaraddy, R.; Zhang, Y.; Demetriadou, A.; Carnegie, C.; Ohadi, H.; De Nijs, B.; Esteban, R.; Aizpurua, J.; Baumberg, J. J. Single-molecule optomechanics in ”picocavities”. Science 2016, 354, 726– 729,  DOI: 10.1126/science.aah5243
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      17
      Single-molecule optomechanics in "picocavities"
      Benz, Felix; Schmidt, Mikolaj K.; Dreismann, Alexander; Chikkaraddy, Rohit; Zhang, Yao; Demetriadou, Angela; Carnegie, Cloudy; Ohadi, Hamid; de Nijs, Bart; Esteban, Ruben; Aizpurua, Javier; Baumberg, Jeremy J.
      Science (Washington, DC, United States) (2016), 354 (6313), 726-729CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Trapping light with noble metal nanostructures overcomes the diffraction limit and can confine light to vols. typically ∼30 cubic nanometers. Individual at. features inside the gap of a plasmonic nanoassembly can localize light to vols. well <1 cubic nanometer (picocavities), enabling optical expts. on the at. scale. These at. features are dynamically formed and disassembled by laser irradn. Although unstable at room temp., picocavities can be stabilized at cryogenic temps., allowing single at. cavities to be probed for many minutes. Unlike traditional optomech. resonators, such extreme optical confinement yields a factor of 106 enhancement of optomech. coupling between the picocavity field and vibrations of individual mol. bonds. This work sets the basis for developing nanoscale nonlinear quantum optics on the single-mol. level.
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    18. 18
      Roelli, P.; Martin-Cano, D.; Kippenberg, T. J.; Galland, C. Molecular Platform for Frequency Upconversion at the Single-Photon Level. Phys. Rev. X 2020, 10, 031057  DOI: 10.1103/PhysRevX.10.031057
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      18
      Molecular Platform for Frequency Upconversion at the Single-Photon Level
      Roelli, Philippe; Martin-Cano, Diego; Kippenberg, Tobias J.; Galland, Christophe
      Physical Review X (2020), 10 (3), 031057CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      Direct detection of single photons at wavelengths beyond 2μm under ambient conditions remains an outstanding technol. challenge. One promising approach is frequency upconversion into the visible (VIS) or near-IR (NIR) domain, where single-photon detectors are readily available. Here, we propose a nanoscale soln. based on a mol. optomech. platform to up-convert photons from the far- and mid-IR (covering part of the terahertz gap) into the VIS-NIR domain. We perform a detailed anal. of its outgoing noise spectral d. and conversion efficiency with a full quantum model. Our platform consists in doubly resonant nanoantennas focusing both the incoming long-wavelength radiation and the short-wavelength pump laser field into the same active region. There, IR active vibrational modes are resonantly excited and couple through their Raman polarizability to the pump field. This optomech. interaction is enhanced by the antenna and leads to the coherent transfer of the incoming low-frequency signal onto the anti-Stokes sideband of the pump laser. Our calcns. demonstrate that our scheme is realizable with current technol. and that optimized platforms can reach single-photon sensitivity in a spectral region where this capability remains unavailable to date.
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    19. 19
      Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W. Entangling Mechanical Motion with Microwave Fields. Science 2013, 342, 710– 713,  DOI: 10.1126/science.1244563
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      Entangling mechanical motion with microwave fields
      Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W.
      Science (Washington, DC, United States) (2013), 342 (6159), 710-713CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      When two phys. systems share the quantum property of entanglement, measurements of one system appear to det. the state of the other. This peculiar property is used in optical, at., and elec. systems in an effort to exceed classical bounds when processing information. The authors extended the domain of this quantum resource by entangling the motion of a macroscopic mech. oscillator with a propagating elec. signal and by storing one half of the entangled state in the mech. oscillator. This result demonstrates an essential requirement for using compact and low-loss micromech. oscillators in a quantum processor, can be extended to sense forces beyond the std. quantum limit, and may enable tests of quantum theory.
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    20. 20
      Palomaki, T. A.; Harlow, J. W.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W. Coherent state transfer between itinerant microwave fields and a mechanical oscillator. Nature 2013, 495, 210– 214,  DOI: 10.1038/nature11915
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      Coherent state transfer between itinerant microwave fields and a mechanical oscillator
      Palomaki, T. A.; Harlow, J. W.; Teufel, J. D.; Simmonds, R. W.; Lehnert, K. W.
      Nature (London, United Kingdom) (2013), 495 (7440), 210-214CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Macroscopic mech. oscillators have been coaxed into a regime of quantum behavior by direct refrigeration or a combination of refrigeration and laser-like cooling. This result supports the idea that mech. oscillators may perform useful functions in the processing of quantum information with superconducting circuits, either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems. As yet, the transfer of an itinerant state or a propagating mode of a microwave field to and from a storage medium has not been demonstrated, owing to the inability to turn on and off the interaction between the microwave field and the medium sufficiently quickly. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mech. oscillator with amplitudes at the single-quantum level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mech. oscillator. In this quantum regime, the mech. oscillator can both store quantum information and enable its transfer between otherwise incompatible systems.
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    21. 21
      Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W. Faithful conversion of propagating quantum information to mechanical motion. Nat. Phys. 2017, 13, 1163– 1167,  DOI: 10.1038/nphys4251
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      Faithful conversion of propagating quantum information to mechanical motion
      Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W.
      Nature Physics (2017), 13 (12), 1163-1167CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
      The motion of micrometre-sized mech. resonators can now be controlled and measured at the fundamental limits imposed by quantum mechanics. These resonators have been prepd. in their motional ground state or in squeezed states, measured with quantum-limited precision, and even entangled with microwave fields. Such advances make it possible to process quantum information using the motion of a macroscopic object. In particular, recent expts. have combined mech. resonators with superconducting quantum circuits to frequency-convert, store and amplify propagating microwave fields. But these systems have not been used to manipulate states that encode quantum bits (qubits), which are required for quantum communication and modular quantum computation. Here we demonstrate the conversion of propagating qubits encoded as superpositions of zero and one photons to the motion of a micromech. resonator with a fidelity in excess of the classical bound. This ability is necessary for mech. resonators to convert quantum information between the microwave and optical domains or to act as storage elements in a modular quantum information processor. Addnl., these results are an important step towards testing speculative notions that quantum theory may not be valid for sufficiently massive systems.
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      Chen, W.; Roelli, P.; Hu, H.; Verlekar, S.; Amirtharaj, S. P.; Barreda, A. I.; Kippenberg, T. J.; Kovylina, M.; Verhagen, E.; Martínez, A.; Galland, C. Continuous-Wave Frequency Upconversion with a Molecular Optomechanical Nanocavity. 2021, arXiv:2107.03033. arXiv.org e-Print archive. https://arxiv.org/abs/2107.03033.
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      Xomalis, A.; Zheng, X.; Chikkaraddy, R.; Koczor-Benda, Z.; Miele, E.; Rosta, E.; Vandenbosch, G. A. E.; Martínez, A.; Baumberg, J. J. Detecting Mid-Infrared Light by Molecular Frequency Upconversion with Dual-Wavelength Hybrid Nanoantennas. 2021, arXiv:2107.02507. arXiv.org e-Print archive. https://arxiv.org/abs/2107.02507.
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      Aspelmeyer, M.; Kippenberg, T. J.; Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 2014, 86, 1391– 1452,  DOI: 10.1103/RevModPhys.86.1391
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      Cohadon, P. F.; Heidmann, A.; Pinard, M. Cooling of a Mirror by Radiation Pressure. Phys. Rev. Lett. 1999, 83, 3174– 3177,  DOI: 10.1103/PhysRevLett.83.3174
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      Cooling of a Mirror by Radiation Pressure
      Cohadon, P. F.; Heidmann, A.; Pinard, M.
      Physical Review Letters (1999), 83 (16), 3174-3177CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We describe an expt. in which a mirror is cooled by the radiation pressure of light. A high-finesse optical cavity with a mirror coated on a mech. resonator is used as an optomech. sensor of the Brownian motion of the mirror. A feedback mechanism controls this motion via the radiation pressure of a laser beam reflected on the mirror. We have obsd. either a cooling or a heating of the mirror, depending on the gain of the feedback loop.
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      Giannini, V.; Fernández-Domínguez, A. I.; Heck, S. C.; Maier, S. A. Plasmonic Nanoantennas: Fundamentals and Their Use in Controlling the Radiative Properties of Nanoemitters. Chem. Rev. 2011, 111, 3888– 3912,  DOI: 10.1021/cr1002672
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      Plasmonic nanoantennas: Fundamentals and their use in controlling the radiative properties of nanoemitters
      Giannini, Vincenzo; Fernandez-Dominguez, Antonio I.; Heck, Susannah C.; Maier, Stefan A.
      Chemical Reviews (Washington, DC, United States) (2011), 111 (6), 3888-3912CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review.
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      Ausman, L. K.; Schatz, G. C. Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons. J. Chem. Phys. 2008, 129, 054704  DOI: 10.1063/1.2961012
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      Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons
      Ausman, Logan K.; Schatz, George C.
      Journal of Chemical Physics (2008), 129 (5), 054704/1-054704/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Calcns. based on the Mie theory are performed to det. the locally enhanced elec. fields due to whispering-gallery mode resonances for dielec. microspheres, with emphasis on electromagnetic hot spots that are located along the wavevector direction on the surface of the sphere. The local elec. field enhancement assocd. with these hot spots is used to det. the surface enhanced Raman scattering enhancement factors for a mol., here treated as a classical dipole, located near the surface of the sphere. Both incident and Raman emission enhancements are calcd. accurately using an extension of the Mie theory that includes interaction of the Raman dipole field with the sphere. The enhancement factors are calcd. for dielec. spheres in vacuum with a refractive index of 1.9 and radii of 5, 10, and 20 μm and for wavelengths that span the visible spectrum. Maximum Raman scattering enhancement factors ∼103-104 are found at locations slightly off the propagation axis when the incident excitation but not the Stokes-shifted radiation is coincident with a whispering-gallery mode resonance. The enhancement factors vary inversely with the resonance width, and this dets. the influence of the mode no. and order on the results. Addnl. calcns. are performed for the case where the Stokes-shifted radiation is on-resonance and Raman enhancement factors as large as 108 are found. These enhancement factors are typically a factor of 102 smaller than would be obtained from |E|4 enhancement ests., as enhancement of the Raman dipole emission is significantly reduced compared to the local field enhancement for micron size particles or larger. Conditions under which single-mol. or few-mol. measurements are feasible are identified. (c) 2008 American Institute of Physics.
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      Foreman, M. R.; Vollmer, F. Level repulsion in hybrid photonic-plasmonic microresonators for enhanced biodetection. Phys. Rev. A 2013, 88, 023831  DOI: 10.1103/PhysRevA.88.023831
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      Level repulsion in hybrid photonic-plasmonic microresonators for enhanced biodetection
      Foreman, Matthew R.; Vollmer, Frank
      Physical Review A: Atomic, Molecular, and Optical Physics (2013), 88 (2-B), 023831/1-023831/6CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
      We theor. analyze photonic-plasmonic coupling between a high-Q whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and red shifts of WGM resonances are shown to arise from crossing of the photonic and plasmonic modes. Level repulsion in the hybrid system is further seen to enable sensitivity enhancements in WGM sensors: maximal when the two resonators are detuned by half the plasmon linewidth. Approx. bounds are given to quantify possible enhancements. Criteria for reactive vs resistive coupling are also established.
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    29. 29
      Thakkar, N.; Rea, M. T.; Smith, K. C.; Heylman, K. D.; Quillin, S. C.; Knapper, K. A.; Horak, E. H.; Masiello, D. J.; Goldsmith, R. H. Sculpting Fano Resonances to Control Photonic-Plasmonic Hybridization. Nano Lett. 2017, 17, 6927– 6934,  DOI: 10.1021/acs.nanolett.7b03332
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      Sculpting Fano Resonances To Control Photonic-Plasmonic Hybridization
      Thakkar, Niket; Rea, Morgan T.; Smith, Kevin C.; Heylman, Kevin D.; Quillin, Steven C.; Knapper, Kassandra A.; Horak, Erik H.; Masiello, David J.; Goldsmith, Randall H.
      Nano Letters (2017), 17 (11), 6927-6934CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Hybrid photonic-plasmonic systems have tremendous potential as versatile platforms for the study and control of nanoscale light-matter interactions since their resp. components have either high-quality factors or low mode vols. Individual metallic nanoparticles deposited on optical microresonators provide an excellent example where ultrahigh-quality optical whispering-gallery modes can be combined with nanoscopic plasmonic mode vols. to maximize the system's photonic performance. Such optimization, however, is difficult in practice because of the inability to easily measure and tune crit. system parameters. In this Letter, we present a general and practical method to det. the coupling strength and tailor the degree of hybridization in composite optical microresonator-plasmonic nanoparticle systems based on exptl. measured absorption spectra. Specifically, we use thermal annealing to control the detuning between a metal nanoparticle's localized surface plasmon resonance and the whispering-gallery modes of an optical microresonator cavity. We demonstrate the ability to sculpt Fano resonance lineshapes in the absorption spectrum and infer system parameters crit. to elucidating the underlying photonic-plasmonic hybridization. We show that including decoherence processes is necessary to capture the evolution of the lineshapes. As a result, thermal annealing allows us to directly tune the degree of hybridization and various hybrid mode quantities such as the quality factor and mode vol. and ultimately maximize the Purcell factor to be 104.
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    30. 30
      Pan, F.; Smith, K. C.; Nguyen, H. L.; Knapper, K. A.; Masiello, D. J.; Goldsmith, R. H. Elucidating Energy Pathways through Simultaneous Measurement of Absorption and Transmission in a Coupled Plasmonic–Photonic Cavity. Nano Lett. 2020, 20, 50– 58,  DOI: 10.1021/acs.nanolett.9b02796
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      Elucidating Energy Pathways through Simultaneous Measurement of Absorption and Transmission in a Coupled Plasmonic-Photonic Cavity
      Pan, Feng; Smith, Kevin C.; Nguyen, Hoang L.; Knapper, Kassandra A.; Masiello, David J.; Goldsmith, Randall H.
      Nano Letters (2020), 20 (1), 50-58CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Control of light-matter interactions is central to numerous advances in quantum communication, information, and sensing. The relative ease with which interactions can be tailored in coupled plasmonic-photonic systems makes them ideal candidates for investigation. To exert control over the interaction between photons and plasmons, it is essential to identify the underlying energy pathways which influence the system's dynamics and det. the crit. system parameters, such as the coupling strength and dissipation rates. However, in coupled systems which dissipate energy through multiple competing pathways, simultaneously resolving all parameters from a single expt. is challenging as typical observables such as absorption and scattering each probe only a particular path. In this work, we simultaneously measure both photothermal absorption and two-sided optical transmission in a coupled plasmonic-photonic resonator consisting of plasmonic gold nanorods deposited on a toroidal whispering-gallery-mode optical microresonator. We then present an anal. model which predicts and explains the distinct line shapes obsd. and quantifies the contribution of each system parameter. By combining this model with expt., we ext. all system parameters with a dynamic range spanning 9 orders of magnitude. Our combined approach provides a full description of plasmonic-photonic energy dynamics in a weakly coupled optical system, a necessary step for future applications that rely on tunability of dissipation and coupling.
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      Frimmer, M.; Koenderink, A. F. Superemitters in hybrid photonic systems: A simple lumping rule for the local density of optical states and its breakdown at the unitary limit. Phys. Rev. B 2012, 86, 235428  DOI: 10.1103/PhysRevB.86.235428
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      Superemitters in hybrid photonic systems: a simple lumping rule for the local density of optical states and its breakdown at the unitary limit
      Frimmer, Martin; Koenderink, A. Femius
      Physical Review B: Condensed Matter and Materials Physics (2012), 86 (23), 235428/1-235428/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We theor. investigate how the enhancement of the radiative decay rate of a spontaneous emitter provided by coupling to an optical antenna is modified when this "superemitter" is introduced into a complex photonic environment that provides an enhanced local d. of optical states (LDOS) itself, such as a microcavity or stratified medium. We show that photonic environments with increased LDOS further boost the performance of antennas that scatter weakly, for which a simple multiplicative LDOS lumping rule holds. In contrast, enhancements provided by antennas close to the unitary limit, i.e., close to the limit of maximally possible scattering strength, are strongly reduced by an enhanced LDOS of the environment. Thus, we identify multiple scattering in hybrid photonic systems as a powerful mechanism for LDOS engineering.
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      Kamandar Dezfouli, M.; Gordon, R.; Hughes, S. Modal theory of modified spontaneous emission of a quantum emitter in a hybrid plasmonic photonic-crystal cavity system. Phys. Rev. A 2017, 95, 013846  DOI: 10.1103/PhysRevA.95.013846
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      Barth, M.; Schietinger, S.; Fischer, S.; Becker, J.; Nüsse, N.; Aichele, T.; Löchel, B.; Sönnichsen, C.; Benson, O. Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling. Nano Lett. 2010, 10, 891– 895,  DOI: 10.1021/nl903555u
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      Nanoassembled Plasmonic-Photonic Hybrid Cavity for Tailored Light-Matter Coupling
      Barth, Michael; Schietinger, Stefan; Fischer, Sabine; Becker, Jan; Nuesse, Nils; Aichele, Thomas; Loechel, Bernd; Soennichsen, Carsten; Benson, Oliver
      Nano Letters (2010), 10 (3), 891-895CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The authors propose and demonstrate a hybrid cavity system in which metal nanoparticles are evanescently coupled to a dielec. photonic crystal cavity using a nanoassembly method. While the metal constituents lead to strongly localized fields, optical feedback is provided by the surrounding photonic crystal structure. The combined effect of plasmonic field enhancement and high quality factor (Q ≈ 900) opens new routes for the control of light-matter interaction at the nanoscale.
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      Gurlek, B.; Sandoghdar, V.; Martín-Cano, D. Manipulation of Quenching in Nanoantenna-Emitter Systems Enabled by External Detuned Cavities: A Path to Enhance Strong-Coupling. ACS Photonics 2018, 5, 456– 461,  DOI: 10.1021/acsphotonics.7b00953
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      Manipulation of Quenching in Nanoantenna-Emitter Systems Enabled by External Detuned Cavities: A Path to Enhance Strong-Coupling
      Gurlek, Burak; Sandoghdar, Vahid; Martin-Cano, Diego
      ACS Photonics (2018), 5 (2), 456-461CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      A broadband Fabry-Perot microcavity can assist an emitter coupled to an off-resonant plasmonic nanoantenna to inhibit the nonradiative channels that affect the quenching of fluorescence. The interference mechanism that creates the necessary enhanced couplings and bandwidth narrowing of the hybrid resonance are identified, and it can assist entering into the strong coupling regime. The results provide new possibilities for improving the efficiency of solid-state emitters and accessing diverse realms of photophysics with hybrid structures that can be fabricated using existing technols.
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      Palstra, I. M.; Doeleman, H. M.; Koenderink, A. F. Hybrid cavity-antenna systems for quantum optics outside the cryostat?. Nanophotonics 2019, 8, 1513– 1531,  DOI: 10.1515/nanoph-2019-0062
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      Hybrid cavity-antenna systems for quantum optics outside the cryostat?
      Palstra, Isabelle M.; Doeleman, Hugo M.; Koenderink, A. Femius
      Nanophotonics (2019), 8 (9), 1513-1531CODEN: NANOLP; ISSN:2192-8614. (Walter de Gruyter GmbH)
      Hybrid cavity-antenna systems have been proposed to combine the sub-wavelength light confinement of plasmonic antennas with microcavity quality factors Q. Here, we examine what confinement and Q can be reached in these hybrid systems, and we address their merits for various applications in classical and quantum optics. Specifically, we investigate their applicability for quantum-optical applications at noncryogenic temps. To this end we first derive design rules for hybrid resonances from a simple anal. model. These rules are benchmarked against full-wave simulations of hybrids composed of state-of-the-art nanobeam cavities and plasmonic-dimer gap antennas. We find that hybrids can outperform the plasmonic and cavity constituents in terms of Purcell factor, and addnl. offer freedom to reach any Q at a similar Purcell factor. We discuss how these metrics are highly advantageous for a high Purcell factor, yet weak-coupling applications, such as bright sources of indistinguishable single photons. The challenges for room-temp. strong coupling, however, are far more daunting: the extremely high dephasing of emitters implies that little benefit can be achieved from trading confinement against a higher Q, as done in hybrids. An attractive alternative could be strong coupling at liq. nitrogen temp., where emitter dephasing is lower and this trade-off can alleviate the stringent fabrication demands required for antenna strong coupling. For few-emitter strong-coupling, high-speed and low-power coherent or incoherent light sources, particle sensing and vibrational spectroscopy, hybrids provide the unique benefit of very high local optical d. of states, tight plasmonic confinement, yet microcavity Q.
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      Doeleman, H. M.; Dieleman, C. D.; Mennes, C.; Ehrler, B.; Koenderink, A. F. Observation of Cooperative Purcell Enhancements in Antenna-Cavity Hybrids. ACS Nano 2020, 14, 12027– 12036,  DOI: 10.1021/acsnano.0c05233
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      Observation of Cooperative Purcell Enhancements in Antenna-Cavity Hybrids
      Doeleman, Hugo M.; Dieleman, Christian D.; Mennes, Christiaan; Ehrler, Bruno; Koenderink, A. Femius
      ACS Nano (2020), 14 (9), 12027-12036CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Localizing light to nanoscale vols. through nanoscale resonators that are low loss and precisely tailored in spectrum to properties of matter is crucial for classical and quantum light sources, cavity QED, mol. spectroscopy, and many other applications. To date, two opposite strategies have been identified: to use either plasmonics with deep subwavelength confinement yet high loss and very poor spectral control or instead microcavities with exquisite quality factors yet poor confinement. In this work we realize hybrid plasmonic-photonic resonators that enhance the emission of single quantum dots, profiting from both plasmonic confinement and microcavity quality factors. Our expts. directly demonstrate how cavity and antenna jointly realize large cooperative Purcell enhancements through interferences. These can be controlled to engineer arbitrary Fano lineshapes in the local d. of optical states.
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      Dezfouli, M. K.; Gordon, R.; Hughes, S. Molecular Optomechanics in the Anharmonic Cavity-QED Regime Using Hybrid Metal-Dielectric Cavity Modes. ACS Photonics 2019, 6, 1400– 1408,  DOI: 10.1021/acsphotonics.8b01091
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      Molecular Optomechanics in the Anharmonic Cavity-QED Regime Using Hybrid Metal-Dielectric Cavity Modes
      Dezfouli, Mohsen Kamandar; Gordon, Reuven; Hughes, Stephen
      ACS Photonics (2019), 6 (6), 1400-1408CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Using carefully designed hybrid metal-dielec. resonators, the authors mol. optomechanics was studied in the strong coupling regime (g2/ωm>κ), which manifests in anharmonic emission lines in the sideband-resolved region of the cavity-emitted spectrum (κ<ωm). This optomech. strong coupling regime is enabled through a metal-dielec. cavity system that yields not only deep sub-wavelength plasmonic confinement, but also dielec.-like confinement times that are >2 orders of magnitude larger than those from typical localized plasmon modes. The classical mode parameters are quantified using quasinormal mode theory, and the quantum dynamics are computed using both std. and generalized quantum master equations. These hybrid metal-dielec. cavity modes enable study of new avenues of quantum plasmonics for single mol. Raman scattering.
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      Ameling, R.; Giessen, H. Microcavity plasmonics: strong coupling of photonic cavities and plasmons. Laser Photonics Rev. 2013, 7, 141– 169,  DOI: 10.1002/lpor.201100041
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      Microcavity plasmonics: strong coupling of photonic cavities and plasmons
      Ameling, Ralf; Giessen, Harald
      Laser & Photonics Reviews (2013), 7 (2), 141-169CODEN: LPRAB8; ISSN:1863-8880. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. The understanding of light-matter interactions at the nanoscale lays the groundwork for many future technologies, applications and materials. The scope of this article is the investigation of coupled photonic-plasmonic systems consisting of a combination of photonic microcavities and metallic nanostructures. In such systems, it is possible to observe an exceptionally strong coupling between electromagnetic light modes of a resonator and collective electron oscillations (plasmons) in the metal. Furthermore, the results have shown that coupled photonic-plasmonic structures possess a considerably higher sensitivity to changes in their environment than conventional localized plasmon sensors due to a plasmon excitation phase shift that depends on the environment.
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      Soltani, S.; Diep, V. M.; Zeto, R.; Armani, A. M. Stimulated Anti-Stokes Raman Emission Generated by Gold Nanorod Coated Optical Resonators. ACS Photonics 2018, 5, 3550– 3556,  DOI: 10.1021/acsphotonics.8b00296
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      Stimulated Anti-Stokes Raman Emission Generated by Gold Nanorod Coated Optical Resonators
      Soltani, Soheil; Diep, Vinh M.; Zeto, Rene; Armani, Andrea M.
      ACS Photonics (2018), 5 (9), 3550-3556CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Plasmonic nanomaterials and nanostructured substrates have made a significant impact in sensing and imaging due to their ability to improve optical field confinement at interfaces. This improved confinement increases the optical field intensity, enabling numerous nonlinear effects to be revealed. One challenge is effectively coupling light into and out of the plasmonic nanomaterial. One approach is to directly integrate the plasmonic nanomaterials onto the surface of light emitting optical devices. The highly nonlinear complex of org. small mol. functionalized Au nanorods is coated on the surface of optical resonators. The evanescent tail of the optical field circulating inside the resonator directly interacts with the nanoparticle complex, creating a hybridized plasmon-whispering gallery mode. Due to the strong field localization by the nanorods and the large circulating power within the resonator, Stimulated Anti-Stokes Raman Scattering is generated with only 14 mW of input power, which is a 4-fold redn. as compared to previous work.
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      Liu, W.; Chen, Y.-L.; Tang, S.-J.; Vollmer, F.; Xiao, Y.-F. Nonlinear Sensing with Whispering-Gallery Mode Microcavities: From Label-Free Detection to Spectral Fingerprinting. Nano Lett. 2021, 21, 1566– 1575,  DOI: 10.1021/acs.nanolett.0c04090
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      Nonlinear Sensing with Whispering-Gallery Mode Microcavities: From Label-Free Detection to Spectral Fingerprinting
      Liu, Wenjing; Chen, You-Ling; Tang, Shui-Jing; Vollmer, Frank; Xiao, Yun-Feng
      Nano Letters (2021), 21 (4), 1566-1575CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      A review. Optical microresonators have attracted intense interests in highly sensitive mol. detection and optical precision measurement in the past decades. In particular, the combination of a high quality factor with a small mode vol. significantly enhances the nonlinear light-matter interaction in whispering-gallery mode (WGM) microresonators, which greatly boost nonlinear optical sensing applications. Nonlinear WGM microsensors not only allow for label-free detection of mols. with an ultrahigh sensitivity but also support new functionalities in sensing such as the specific spectral fingerprinting of mols. with frequency conversion involved. Here, we review the mechanisms, sensing modalities, and recent progresses of nonlinear optical sensors along with a brief outlook on the possible future research directions of this rapidly advancing field.
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      Peyskens, F.; Dhakal, A.; Van Dorpe, P.; Le Thomas, N.; Baets, R. Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform. ACS Photonics 2016, 3, 102– 108,  DOI: 10.1021/acsphotonics.5b00487
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      Surface Enhanced Raman Spectroscopy Using a Single Mode Nanophotonic-Plasmonic Platform
      Peyskens, Frederic; Dhakal, Ashim; Van Dorpe, Pol; Le Thomas, Nicolas; Baets, Roel
      ACS Photonics (2016), 3 (1), 102-108CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      We demonstrate the generation of Surface Enhanced Raman Spectroscopy (SERS) signals from integrated bowtie antennas, excited and collected by the fundamental TE mode of a single mode silicon nitride waveguide. Due to the integrated nature of this particular single mode SERS probe one can rigorously quantify the complete enhancement process. The Stokes power, generated by a 4-nitrothiophenol-coated antenna and collected into the fundamental TE mode, exhibits an 8 × 106 enhancement compared to the free space Raman scattering of a 4-nitrothiophenol mol. Furthermore, we present an anal. model which identifies the relevant design parameters and figure of merit for this new SERS-platform. An excellent correspondence is obtained between the theor. predicted and exptl. obsd. abs. Raman power. This work paves the way toward a new class of fully integrated lab-on-a-chip systems where the single mode SERS probe can be combined with other photonic, fluidic, or biol. functionalities.
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      Doeleman, H. M.; Verhagen, E.; Koenderink, A. F. Antenna-Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth. ACS Photonics 2016, 3, 1943– 1951,  DOI: 10.1021/acsphotonics.6b00453
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      Antenna-Cavity Hybrids: Matching Polar Opposites for Purcell Enhancements at Any Linewidth
      Doeleman, Hugo M.; Verhagen, Ewold; Koenderink, A. Femius
      ACS Photonics (2016), 3 (10), 1943-1951CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Strong interaction between light and a single quantum emitter is essential to a great no. of applications, including single photon sources. Microcavities and plasmonic antennas have been used frequently to enhance these interactions through the Purcell effect. Both can provide large emission enhancements: the cavity typically through long photon lifetimes (high Q), and the antenna mostly through strong field enhancement (low mode vol. V). In this work, we demonstrate that a hybrid system, which combines a cavity and a dipolar antenna, can achieve stronger emission enhancements than the cavity or antenna alone. We show that these systems can in fact break the fundamental limit on single antenna enhancement. Addnl., hybrid systems can be used as a versatile platform to tune the bandwidth of enhancement to any desired value between that of the cavity and the antenna, while simultaneously boosting emission enhancement. Our fully self-consistent anal. model allows to identify the underlying mechanisms of boosted emission enhancement in hybrid systems, which include radiation damping and constructive interference between multiple-scattering paths. Moreover, we find excellent agreement between strongly boosted enhancement spectra from our anal. model and from finite-element simulations on a realistic cavity-antenna system. Finally, we demonstrate that hybrid systems can simultaneously boost emission enhancement and maintain a near-unity outcoupling efficiency into a single cavity decay channel, such as a waveguide.
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      Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals
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      An introduction is given to the theory of inelastic light scattering by polaritons in dielec. crystals. The treatment is based on a simple 2-oscillator model which represents the ionic and electronic motions of a crystal. The model contains a 3rd-order anharmonicity which allows an incident laser beam to mix with the oscillator fluctuations and produce scattered light of frequency different from the incident frequency. The magnitude of the oscillator fluctuations is detd. by an application of the Nyquist or fluctuation-dissipation theorem, by using the response functions of the oscillators for externally applied forces. The simple model gives results for light scattering cross sections which agree with more rigorous derivations in the existing literature. The response function approach is generalized to apply to crystals having many ionic resonances and of uniaxial or orthorhombic structure. The general formulas reduce in appropriate special cases to results already published. Exptl. and theoretical work on light scattering by polaritons and by pure phonons is reviewed in the context of both the 2-oscillator model and the general theory. Particular attention is given to resonance scattering in an attempt to achieve consistency between the differing theoretical treatments in the literature. The subject matter of the review overlaps some topics in nonlinear optics, and contact is made with the theories of the electrooptic effect and stimulated Raman scattering.
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      Rapid progress in photonics and nanotechnol. brings many examples of resonant optical phenomena assocd. with the physics of Fano resonances, with applications in optical switching and sensing. For successful design of photonic devices, it is important to gain deep insight into different resonant phenomena and understand their connection. Here, we review a broad range of resonant electromagnetic effects by using two effective coupled oscillators, including the Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity-time symmetry breaking. We discuss how to introduce the Fano parameter for describing a transition between two seemingly different spectroscopic signatures assocd. with asym. Fano and sym. Lorentzian shapes. We also review the recent results on Fano resonances in dielec. nanostructures and metasurfaces.
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      Xomalis, A.; Chikkaraddy, R.; Oksenberg, E.; Shlesinger, I.; Huang, J.; Garnett, E. C.; Koenderink, A. F.; Baumberg, J. J. Controlling Optically Driven Atomic Migration Using Crystal-Facet Control in Plasmonic Nanocavities. ACS Nano 2020, 14, 10562– 10568,  DOI: 10.1021/acsnano.0c04600
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      Controlling Optically Driven Atomic Migration Using Crystal-Facet Control in Plasmonic Nanocavities
      Xomalis, Angelos; Chikkaraddy, Rohit; Oksenberg, Eitan; Shlesinger, Ilan; Huang, Junyang; Garnett, Erik C.; Koenderink, A. Femius; Baumberg, Jeremy J.
      ACS Nano (2020), 14 (8), 10562-10568CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Plasmonic nanoconstructs are widely exploited to confine light for applications ranging from quantum emitters to medical imaging and biosensing. However, accessing extreme near-field confinement using the surfaces of metallic nanoparticles often induces permanent structural changes from light, even at low intensities. Here, we report a robust and simple technique to exploit crystal facets and their at. boundaries to prevent the hopping of atoms along and between facet planes. Avoiding X-ray or electron microscopy techniques that perturb these at. restructurings, we use elastic and inelastic light scattering to resolve the influence of crystal habit. A clear increase in stability is found for {100} facets with steep inter-facet angles, compared to multiple at. steps and shallow facet curvature on spherical nanoparticles. Avoiding at. hopping allows Raman scattering on mols. with low Raman cross-section while circumventing effects of charging and adatom binding, even over long measurement times. These nanoconstructs allow the optical probing of dynamic reconstruction in nanoscale surface science, photocatalysis, and mol. electronics.
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      A review. Optical microcavities confine light to small vols. by resonant recirculation. Devices based on optical microcavities are already indispensable for a wide range of applications and studies. For example, microcavities made of active III-V semiconductor materials control laser emission spectra to enable long-distance transmission of data over optical fibers; they also ensure narrow spot-size laser read/write beams in CD and DVD players. In quantum optical devices, microcavities can coax atoms or quantum dots to emit spontaneous photons in a desired direction or can provide an environment where dissipative mechanisms such as spontaneous emission are overcome so that quantum entanglement of radiation and matter is possible. Applications of these remarkable devices are as diverse as their geometrical and resonant properties.
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      Ordered, org. monolayers were formed on Au slides by adsorption from EtOH of HS(CH2)10CH2OH, HS(CH2)10CH3, [S(CH2)10CH2OH]2, [S(CH2)10CH3]2, and binary mixts. of these mols. in which 1 component was terminated by a hydrophobic Me group and 1 by a hydrophilic alc. group. The compns. of the monolayers were detd. by XPS. Wettability was used as a probe of the chem. compn. and structure of the surface of the monolayer. When monolayers were formed in solns. contg. mixts. of a thiol and a disulfide, adsorption of the thiol was strongly preferred (∼75:1). The advancing contact angles of water and hexadecane on monolayers formed from solns. contg. mixts. of 2 thiols, a thiol and a disulfide, or 2 disulfides depend on the proportion of OH-terminated chains in the monolayer and are largely independent of the nature of the precursor species. This observation suggests that both thiols and disulfides give rise to the same chem. species (probably a thiolate) on the surface. This model is supported by the observation by XPS of indistinguishable S(2p) signals from monolayers derived from thiols and disulfides.
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      Yanay, Y.; Clerk, A. A. Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation. Phys. Rev. A 2018, 98, 043615  DOI: 10.1103/PhysRevA.98.043615
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      Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation
      Yanay, Yariv; Clerk, Aashish A.
      Physical Review A (2018), 98 (4), 043615CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
      We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly dets. the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.
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      Kapfinger, S.; Reichert, T.; Lichtmannecker, S.; Müller, K.; Finley, J. J.; Wixforth, A.; Kaniber, M.; Krenner, H. J. Dynamic Acousto-Optic Control of a Strongly Coupled Photonic Molecule. Nat. Commun. 2015, 6, 8540  DOI: 10.1038/ncomms9540
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      Dynamic acousto-optic control of a strongly coupled photonic molecule
      Kapfinger, Stephan; Reichert, Thorsten; Lichtmannecker, Stefan; Mueller, Kai; Finley, Jonathan J.; Wixforth, Achim; Kaniber, Michael; Krenner, Hubert J.
      Nature Communications (2015), 6 (), 8540CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Strongly confined photonic modes can couple to quantum emitters and mech. excitations. To harness the full potential in quantum photonic circuits, interactions between different constituents have to be precisely and dynamically controlled. Here, a prototypical coupled element, a photonic mol. defined in a photonic crystal membrane, is controlled by a radio frequency surface acoustic wave. The sound wave is tailored to deliberately switch on and off the bond of the photonic mol. on sub-nanosecond timescales. In time-resolved expts., the acousto-optically controllable coupling is directly obsd. as clear anticrossings between the two nanophotonic modes. The coupling strength is detd. directly from the exptl. data. Both the time dependence of the tuning and the inter-cavity coupling strength are found to be in excellent agreement with numerical calcns. The demonstrated mech. technique can be directly applied for dynamic quantum gate operations in state-of-the-art-coupled nanophotonic, quantum cavity electrodynamic and optomech. systems.
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      Schönleber, D. W.; Eisfeld, A.; El-Ganainy, R. Optomechanical Interactions in Non-Hermitian Photonic Molecules. New J. Phys. 2016, 18, 045014  DOI: 10.1088/1367-2630/18/4/045014
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      Grudinin, I. S.; Lee, H.; Painter, O.; Vahala, K. J. Phonon Laser Action in a Tunable Two-Level System. Phys. Rev. Lett. 2010, 104, 083901  DOI: 10.1103/PhysRevLett.104.083901
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      Phonon Laser Action in a Tunable Two-Level System
      Grudinin, Ivan S.; Lee, Hansuek; Painter, O.; Vahala, Kerry J.
      Physical Review Letters (2010), 104 (8), 083901/1-083901/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The phonon analog of an optical laser has long been a subject of interest. The authors demonstrate a compd. microcavity system, coupled to a radiofrequency mech. mode, that operates in close analogy to a two-level laser system. An inversion produces gain, causing phonon laser action above a pump power threshold of ∼7 μW. The device features a continuously tunable gain spectrum to selectively amplify mech. modes from radio frequency to microwave rates. Viewed as a Brillouin process, the system accesses a regime in which the phonon plays what has traditionally been the role of the Stokes wave. For this reason, it should also be possible to controllably switch between phonon and photon laser regimes. Cooling of the mech. mode is also possible.
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      Jing, H.; Özdemir, S. K.; Lü, X.-Y.; Zhang, J.; Yang, L.; Nori, F. PT-Symmetric Phonon Laser. Phys. Rev. Lett. 2014, 113, 053604  DOI: 10.1103/PhysRevLett.113.053604
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      PT-symmetric phonon laser
      Jing, Hui; Ozdemir, S. K.; Lu, Xin-You; Zhang, Jing; Yang, Lan; Nori, Franco
      Physical Review Letters (2014), 113 (5), 053604CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      By exploiting recent developments assocd. with coupled microcavities, we introduce the concept of PT-sym. phonon laser with balanced gain and loss. This is accomplished by introducing gain to one of the microcavities such that it balances the passive loss of the other. In the vicinity of the gain-loss balance, a strong nonlinear relation emerges between the intracavity-photon intensity and the input power. This then leads to a giant enhancement of both optical pressure and mech. gain, resulting in a highly efficient phonon-lasing action. These results provide a promising approach for manipulating optomech. systems through PT-sym. concepts. Potential applications range from enhancing mech. cooling to designing phonon-laser amplifiers.
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      Lü, H.; Özdemir, S. K.; Kuang, L.-M.; Nori, F.; Jing, H. Exceptional Points in Random-Defect Phonon Lasers. Phys. Rev. Appl. 2017, 8, 044020  DOI: 10.1103/PhysRevApplied.8.044020
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      Exceptional points in random-defect phonon lasers
      Lue, H.; Oezdemir, S. K.; Kuang, L.-M.; Nori, Franco; Jing, H.
      Physical Review Applied (2017), 8 (4), 044020/1-044020/9CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
      Intrinsic defects in optomech. devices are generally viewed to be detrimental for achieving coherent amplification of phonons, and great care has thus been exercised in fabricating devices and materials with no (or a minimal no. of) defects. Contrary to this view, here we show that, by surpassing an exceptional point (EP), both the mech. gain and the phonon no. can be enhanced despite increasing defect losses. This counterintuitive effect, well described by an effective non-Hermitian phonon-defect model, provides a mech. analog of the loss-induced purely optical lasing. This opens the way to operating random-defect phonon devices at EPs.
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      Zhang, J.; Peng, B.; Özdemir, Ş. K.; Pichler, K.; Krimer, D. O.; Zhao, G.; Nori, F.; Liu, Y.-x.; Rotter, S.; Yang, L. A Phonon Laser Operating at an Exceptional Point. Nat. Photonics 2018, 12, 479– 484,  DOI: 10.1038/s41566-018-0213-5
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      A phonon laser operating at an exceptional point
      Zhang, Jing; Peng, Bo; Ozdemir, Sahin Kaya; Pichler, Kevin; Krimer, Dmitry O.; Zhao, Guangming; Nori, Franco; Liu, Yu-xi; Rotter, Stefan; Yang, Lan
      Nature Photonics (2018), 12 (8), 479-484CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
      Non-Hermitian phys. systems have attracted considerable attention lately for their unconventional behavior around exceptional points (EPs)-spectral singularities at which eigenvalues and eigenvectors coalesce. In particular, many new EP-related concepts such as unidirectional lasing and invisibility, as well as chiral transmission, have been realized. Given the progress in understanding the physics of EPs in various photonic structures, it is surprising that one of the oldest theor. predictions assocd. with them, a remarkable broadening of the laser linewidth at an EP, has been probed only indirectly so far. Here, we fill this gap by steering a phonon laser through an EP in a compd. optomech. system formed by two coupled resonators. We observe a pronounced linewidth broadening of the mech. lasing mode generated in one of the resonators when the system approaches the EP.
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      Liew, T. C. H.; Savona, V. Single Photons from Coupled Quantum Modes. Phys. Rev. Lett. 2010, 104, 183601  DOI: 10.1103/PhysRevLett.104.183601
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      Single photons from coupled quantum modes
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      Physical Review Letters (2010), 104 (18), 183601/1-183601/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Single photon emitters often rely on a strong nonlinearity to make the behavior of a quantum mode susceptible to a change in the no. of quanta between one and two. In most systems, the strength of nonlinearity is weak, such that changes at the single quantum level have little effect. Here, we consider coupled quantum modes and find that they can be strongly sensitive at the single quantum level, even if nonlinear interactions are modest. As examples, we consider solid-state implementations based on the tunneling of polaritons between quantum boxes or their parametric modes in a microcavity. We find that these systems can act as promising single photon emitters.
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      Snijders, H. J.; Frey, J. A.; Norman, J.; Flayac, H.; Savona, V.; Gossard, A. C.; Bowers, J. E.; van Exter, M. P.; Bouwmeester, D.; Löffler, W. Observation of the Unconventional Photon Blockade. Phys. Rev. Lett. 2018, 121, 043601  DOI: 10.1103/PhysRevLett.121.043601
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      Observation of the Unconventional Photon Blockade
      Snijders, H. J.; Frey, J. A.; Norman, J.; Flayac, H.; Savona, V.; Gossard, A. C.; Bowers, J. E.; van Exter, M. P.; Bouwmeester, D.; Loeffler, W.
      Physical Review Letters (2018), 121 (4), 043601CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to the conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is obsd. We find a min. second-order correlation g(2)(0)≈0.37, which corresponds to g(2)(0)≈0.005 when cor. for detector jitter, and observe the expected polarization dependency and photon bunching and antibunching; close by in parameter space, which indicates the abrupt change from phase to amplitude squeezing.
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      Vaneph, C.; Morvan, A.; Aiello, G.; Féchant, M.; Aprili, M.; Gabelli, J.; Estève, J. Observation of the Unconventional Photon Blockade in the Microwave Domain. Phys. Rev. Lett. 2018, 121, 043602  DOI: 10.1103/PhysRevLett.121.043602
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      Observation of the Unconventional Photon Blockade in the Microwave Domain
      Vaneph, Cyril; Morvan, Alexis; Aiello, Gianluca; Fechant, Mathieu; Aprili, Marco; Gabelli, Julien; Esteve, Jerome
      Physical Review Letters (2018), 121 (4), 043602CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      We have obsd. the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function g(2)(t) of the microwave field inside one of the two resonators. The lowest measured value of g(2)(0) is 0.4 for a resonator population of approx. 10-2 photons. The time evolution of g(2)(t) exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade.
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      Li, B.; Huang, R.; Xu, X.; Miranowicz, A.; Jing, H. Nonreciprocal Unconventional Photon Blockade in a Spinning Optomechanical System. Photonics Res. 2019, 7, 630,  DOI: 10.1364/PRJ.7.000630
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      Nonreciprocal unconventional photon blockade in a spinning optomechanical system
      Li, Baijun; Huang, Ran; Xu, Xunwei; Miranowicz, Adam; Jing, Hui
      Photonics Research (2019), 7 (6), 630-641CODEN: PRHEIZ; ISSN:2327-9125. (Optical Society of America)
      We propose how to achieve quantum nonreciprocity via unconventional photon blockade (UPB) in a compd. device consisting of an optical harmonic resonator and a spinning optomech. resonator. We show that, even with very weak single-photon nonlinearity, nonreciprocal UPB can emerge in this system, i.e., strong photon antibunching can emerge only by driving the device from one side but not from the other side. This nonreciprocity results from the Fizeau drag, leading to different splitting of the resonance frequencies for the optical counter-circulating modes. Such quantum nonreciprocal devices can be particularly useful in achieving back-action-free quantum sensing or chiral photonic communications.
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